[ { "id": "https://authors.library.caltech.edu/records/r3t9j-wjw61", "eprint_id": 119555, "eprint_status": "archive", "datestamp": "2023-08-22 18:59:13", "lastmod": "2023-10-25 15:35:46", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Collins-Tristan-C", "name": { "family": "Collins", "given": "Tristan C." }, "orcid": "0000-0002-1127-0458" }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Picard-Sebastien", "name": { "family": "Picard", "given": "Sebastien" }, "orcid": "0000-0001-9015-8976" }, { "id": "Yau-Shing-Tung", "name": { "family": "Yau", "given": "Shing-Tung" }, "orcid": "0000-0003-3394-2187" } ] }, "title": "Special Lagrangian Cycles and Calabi-Yau Transitions", "ispublished": "pub", "full_text_status": "public", "keywords": "Mathematical Physics; Statistical and Nonlinear Physics", "note": "Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. \n\nT.C.C is supported in part by NSF CAREER Grant DMS-194452 and an Alfred P. Sloan Fellowship. \n\nS.G. is supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632, and by the National Science Foundation under Grant No. NSF DMS 1664227.", "abstract": "We construct special Lagrangian 3-spheres in non-K\u00e4hler compact threefolds equipped with the Fu\u2013Li\u2013Yau geometry. These non-K\u00e4hler geometries emerge from topological transitions of compact Calabi-Yau threefolds. From this point of view, a conifold transition exchanges holomorphic 2-cycles for special Lagrangian 3-cycles.", "date": "2023-05-03", "date_type": "published", "publication": "Communications in Mathematical Physics", "publisher": "Springer", "id_number": "CaltechAUTHORS:20230227-88449200.41", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20230227-88449200.41", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-194452" }, { "agency": "Alfred P. Sloan Foundation" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "NSF", "grant_number": "DMS-1664227" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" } ] }, "doi": "10.1007/s00220-023-04655-3", "resource_type": "article", "pub_year": "2023", "author_list": "Collins, Tristan C.; Gukov, Sergei; et el." }, { "id": "https://authors.library.caltech.edu/records/br2f4-g6b80", "eprint_id": 120730, "eprint_status": "archive", "datestamp": "2023-08-22 20:23:18", "lastmod": "2023-10-23 20:21:02", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Costantino-Francesco", "name": { "family": "Costantino", "given": "Francesco" } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Putrov-Pavel", "name": { "family": "Putrov", "given": "Pavel" }, "orcid": "0000-0002-7207-4688" } ] }, "title": "Non-Semisimple TQFT's and BPS q-Series", "ispublished": "pub", "full_text_status": "public", "keywords": "Geometry and Topology; Mathematical Physics; Analysis", "note": "The authors retain the copyright for their papers published in SIGMA under the terms of the Creative Commons Attribution-ShareAlike License. \n\nContribution to the Special Issue on Enumerative and Gauge-Theoretic Invariants in honor of Lothar G\u00f6ttsche on the occasion of his 60th birthday. The full collection is available at\nhttps://www.emis.de/journals/SIGMA/Gottsche.html \n\nWe would like to thank Francesco Benini, Christian Copetti, Boris Feigin, Azat Gainutdinov, Hiraku Nakajima, Sunghyuk Park, Du Pei, and Nicolai Reshetikhin for helpful discussions and the anonymous Referees for the valuable suggestions on the improvement of the paper. We also would like to thank the organizers of the 2019 conference \"New Developments in Quantum Topology\" at UC Berkeley, where the discussion on the relation between the two invariants was initiated. The work of S.G. is supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award no. DE-SC0011632, and by the National Science Foundation under Grant no. NSF DMS 1664227. The work of F.C. was supported by the French Agence Nationale de la Recherche via the ANR Project QUANTACT and by the Labex CIMI ANR-11-LABX-0040.\n\n
Published - sigma23-010.pdf
", "abstract": "We propose and in some cases prove a precise relation between 3-manifold invariants associated with quantum groups at roots of unity and at generic q. Both types of invariants are labeled by extra data which plays an important role in the proposed relation. Bridging the two sides - which until recently were developed independently, using very different methods - opens many new avenues. In one direction, it allows to study (and perhaps even to formulate) q-series invariants labeled by spin\u1d9c structures in terms of non-semisimple invariants. In the opposite direction, it offers new insights and perspectives on various elements of non-semisimple TQFT's, bringing the latter into one unifying framework with other invariants of knots and 3-manifolds that recently found realization in quantum field theory and in string theory.", "date": "2023-03-15", "date_type": "published", "publication": "Symmetry, Integrability and Geometry, Methods and Applications (SIGMA)", "volume": "19", "publisher": "Institute of Mathematics of National Academy of Sciences of Ukraine", "pagerange": "Art. No. 10", "id_number": "CaltechAUTHORS:20230411-695015900.13", "issn": "1815-0659", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20230411-695015900.13", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "NSF", "grant_number": "DMS-1664227" }, { "agency": "Agence Nationale de la Recherche (ANR)", "grant_number": "ANR-11-LABX-0040" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" } ] }, "doi": "10.3842/sigma.2023.010", "primary_object": { "basename": "sigma23-010.pdf", "url": "https://authors.library.caltech.edu/records/br2f4-g6b80/files/sigma23-010.pdf" }, "resource_type": "article", "pub_year": "2023", "author_list": "Costantino, Francesco; Gukov, Sergei; et el." }, { "id": "https://authors.library.caltech.edu/records/1a03j-3p565", "eprint_id": 119319, "eprint_status": "archive", "datestamp": "2023-08-20 08:58:52", "lastmod": "2023-10-23 15:31:13", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Lee-Vincent-S-H", "name": { "family": "Lee", "given": "Vincent S.\u2009H." }, "orcid": "0000-0002-3481-3590" }, { "id": "Zurek-K-M", "name": { "family": "Zurek", "given": "Kathryn M." }, "orcid": "0000-0002-2629-337X" } ] }, "title": "Near-horizon quantum dynamics of 4D Einstein gravity from 2D Jackiw-Teitelboim gravity", "ispublished": "pub", "full_text_status": "public", "note": "Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. \n\nFunded by SCOAP3.\n\nWe thank Tom Banks, Temple He, Cynthia Keeler, Juan Maldacena, Allic Sivaramakrishnan, and Erik Verlinde for discussion on these directions. K.\u2009Z. and V.\u2009L. are supported by the Heising-Simons Foundation \"Observational Signatures of Quantum Gravity\" collaboration Grant No. 2021-2817, and by a Simons Investigator award. The work of S.\u2009G. and K.\u2009Z. is supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632.\n\nPublished - PhysRevD.107.016004.pdf
", "abstract": "We study quantum fluctuations in the light-cone metric of the 4D Einstein-Hilbert action via dimensional reduction to Jackiw-Teitelboim (JT) gravity. In particular, we show that, in Einstein gravity, the causal development of a region in flat Minkowski spacetime, near a horizon defined by light sheets, can be described by an effective two-dimensional dilaton theory. This enables us to make use of known solutions of the JT action, where the spacetime position of a horizon has quantum uncertainty due to metric fluctuations. This quantum uncertainty can be then directly related to the original 4D light-cone coordinates, allowing us to compute the uncertainty in the time of a photon to travel from tip-to-tip of a causal diamond in flat 4D Minkowski space. We find that both Planck and infrared scales (with the latter set by the size of the causal diamond) enter the uncertainty in photon travel time, such that the quantum fluctuation in the arrival time may be observably large.", "date": "2023-01-01", "date_type": "published", "publication": "Physical Review D", "volume": "107", "number": "1", "publisher": "American Physical Society", "pagerange": "Art. No. 016004", "id_number": "CaltechAUTHORS:20230217-513857800.4", "issn": "2470-0010", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20230217-513857800.4", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Heising-Simons Foundation", "grant_number": "2021-2817" }, { "agency": "Simons Foundation" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "SCOAP3" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" } ] }, "doi": "10.1103/physrevd.107.016004", "primary_object": { "basename": "PhysRevD.107.016004.pdf", "url": "https://authors.library.caltech.edu/records/1a03j-3p565/files/PhysRevD.107.016004.pdf" }, "resource_type": "article", "pub_year": "2023", "author_list": "Gukov, Sergei; Lee, Vincent S.\u2009H.; et el." }, { "id": "https://authors.library.caltech.edu/records/ctnf1-pzc81", "eprint_id": 116274, "eprint_status": "archive", "datestamp": "2023-08-22 17:20:43", "lastmod": "2023-10-24 21:04:06", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ekholm-Tobias", "name": { "family": "Ekholm", "given": "Tobias" }, "orcid": "0000-0003-2060-8462" }, { "id": "Gruen-Angus", "name": { "family": "Gruen", "given": "Angus" }, "orcid": "0000-0003-0284-009X" }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Kucharski-Piotr", "name": { "family": "Kucharski", "given": "Piotr" }, "orcid": "0000-0002-9599-5658" }, { "id": "Park-Sunghyuk", "name": { "family": "Park", "given": "Sunghyuk" }, "orcid": "0000-0002-6132-0871" }, { "id": "Su\u0142kowski-Piotr", "name": { "family": "Su\u0142kowski", "given": "Piotr" }, "orcid": "0000-0002-6176-6240" } ] }, "title": "\u1e90 at Large N: From Curve Counts to Quantum Modularity", "ispublished": "pub", "full_text_status": "public", "keywords": "Mathematical Physics; Statistical and Nonlinear Physics", "note": "\u00a9 The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2022. \n\nReceived: 7 June 2020 / Accepted: 29 June 2022. \n\nWe would like to thank Sibasish Banerjee, Miranda Cheng, Luis Diogo, Boris Feigin, Francesca Ferrari, Sarah Harrison, Jakub Jankowski, Pietro Longhi, Ciprian Manolescu, Marko Sto\u0161i\u0107, Cumrun Vafa, and Don Zagier for insightful discussions and comments on the draft. The work of T.E. is supported by the Knut and Alice Wallenberg Foundation KAW2020.0307 and by the Swedish Research Council VR2020-04535. The work of S.G. is supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632, and by the National Science Foundation under Grant No. NSF DMS 1664240. The work of P.K. is supported by the Polish Ministry of Science and Higher Education through its programme Mobility Plus (decision no. 1667/MOB/V/2017/0). The research of S.P. is supported by Kwanjeong Educational Foundation. The work of P.S. is supported by the TEAM programme of the Foundation for Polish Science co-financed by the European Union under the European Regional Development Fund (POIR.04.04.00-00-5C55/17-00).\n\nSubmitted - 2005.13349.pdf
", "abstract": "Reducing a 6d fivebrane theory on a 3-manifold Y gives a q-series 3-manifold invariant \u1e91(Y). We analyse the large-N behaviour of F_K = \u1e90(M_K), where M_K is the complement of a knot K in the 3-sphere, and explore the relationship between an a-deformed (a = q\u1d3a) version of F_K and HOMFLY-PT polynomials. On the one hand, in combination with counts of holomorphic annuli on knot complements, this gives an enumerative interpretation of F_K in terms of counts of open holomorphic curves. On the other, it leads to closed form expressions for a-deformed F_K for (2,2p+1)-torus knots. They suggest a further t-deformation based on superpolynomials, which can be used to obtain a t-deformation of ADO polynomials, expected to be related to categorification. Moreover, studying how F_K transforms under natural geometric operations on K indicates relations to quantum modularity in a new setting.", "date": "2022-08-16", "date_type": "published", "publication": "Communications in Mathematical Physics", "publisher": "Springer", "id_number": "CaltechAUTHORS:20220812-829381000", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20220812-829381000", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Knut and Alice Wallenberg Foundation", "grant_number": "KAW2020.0307" }, { "agency": "Swedish Research Council", "grant_number": "VR2020-04535" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "NSF", "grant_number": "DMS-1664240" }, { "agency": "Ministry of Science and Higher Education (Poland)", "grant_number": "1667/MOB/V/2017/0" }, { "agency": "Kwanjeong Educational Foundation" }, { "agency": "Foundation for Polish Science" }, { "agency": "European Regional Development Fund", "grant_number": "POIR.04.04.00-00-5C55/17-00" } ] }, "doi": "10.1007/s00220-022-04469-9", "primary_object": { "basename": "2005.13349.pdf", "url": "https://authors.library.caltech.edu/records/ctnf1-pzc81/files/2005.13349.pdf" }, "resource_type": "article", "pub_year": "2022", "author_list": "Ekholm, Tobias; Gruen, Angus; et el." }, { "id": "https://authors.library.caltech.edu/records/cymfh-sq376", "eprint_id": 114255, "eprint_status": "archive", "datestamp": "2023-08-22 16:27:19", "lastmod": "2023-10-23 23:27:15", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ekholm-Tobias", "name": { "family": "Ekholm", "given": "Tobias" }, "orcid": "0000-0003-2060-8462" }, { "id": "Gruen-Angus", "name": { "family": "Gruen", "given": "Angus" }, "orcid": "0000-0003-0284-009X" }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Kucharski-Piotr", "name": { "family": "Kucharski", "given": "Piotr" }, "orcid": "0000-0002-9599-5658" }, { "id": "Park-Sunghyuk", "name": { "family": "Park", "given": "Sunghyuk" }, "orcid": "0000-0002-6132-0871" }, { "id": "Sto\u0161i\u0107-Marko", "name": { "family": "Sto\u0161i\u0107", "given": "Marko" }, "orcid": "0000-0002-4464-396X" }, { "id": "Su\u0142kowski-Piotr", "name": { "family": "Su\u0142kowski", "given": "Piotr" }, "orcid": "0000-0002-6176-6240" } ] }, "title": "Branches, quivers, and ideals for knot complements", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Quantum invariants; A polynomial; Open curve counts; Geometry and Topology; General Physics and Astronomy; Mathematical Physics", "note": "\u00a9 2022 Elsevier. \n\nReceived 21 December 2021, Accepted 25 March 2022, Available online 1 April 2022, Version of Record 12 April 2022. \n\nP.K. was supported by the Polish Ministry of Education and Science through its programme Mobility Plus (decision number 1667/MOB/V/2017/0) and by NWO vidi grant (number 016.Vidi.189.182). S.P. was partially supported by junior fellowship at Institut Mittag-Leffler and by Kwanjeong Educational Foundation. The work of M.S. was supported by the Portuguese Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia (FCT) through the grant 'Higher Structures and Applications', no. PTDC/MAT-PUR/31089/2017, and FCT Exploratory Grant IF/0998/2015, and by the Ministry of Education, Science and Technological Development of the Republic of Serbia through Mathematical Institute SANU. In the final stages, his work was supported by the Science Fund of the Republic of Serbia, Grant No. 7749891, Graphical Languages \u2013 GWORDS. The work of P.S. was supported by the TEAM programme of the Foundation for Polish Science co-financed by the European Union under the European Regional Development Fund (POIR.04.04.00-00-5C55/17-00). T.E. is supported by the Knut and Alice Wallenberg Foundation as a Wallenberg scholar KAW2020.0307 and by the Swedish Research Council VR2020-04535. The work of S.G. is supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632, and by the National Science Foundation under Grant No. NSF DMS 1664227.", "abstract": "We generalize the F_K invariant, i.e. \u1e90 for the complement of a knot K in the 3-sphere, the knots-quivers correspondence, and A-polynomials of knots, and find several interconnections between them. We associate an F_K invariant to any branch of the A-polynomial of K and we work out explicit expressions for several simple knots. We show that these F_K invariants can be written in the form of a quiver generating series, in analogy with the knots-quivers correspondence. We discuss various methods to obtain such quiver representations, among others using R-matrices. We generalize the quantum a-deformed A-polynomial to an ideal that contains the recursion relation in the group rank, i.e. in the parameter a, and describe its classical limit in terms of the Coulomb branch of a 3d-5d theory. We also provide t-deformed versions. Furthermore, we study how the quiver formulation for closed 3-manifolds obtained by surgery leads to the superpotential of 3d N = 2 theory T[M\u2083] and to the data of the associated modular tensor category MTC[M\u2083].", "date": "2022-07", "date_type": "published", "publication": "Journal of Geometry and Physics", "volume": "177", "publisher": "Elsevier", "pagerange": "Art. No. 104520", "id_number": "CaltechAUTHORS:20220412-15486000", "issn": "0393-0440", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20220412-15486000", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Ministry of Education and Science (Poland)", "grant_number": "1667/MOB/V/2017/0" }, { "agency": "Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO)", "grant_number": "016.Vidi.189.182" }, { "agency": "Institut Mittag-Leffler" }, { "agency": "Kwanjeong Educational Foundation" }, { "agency": "Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia (FCT)", "grant_number": "PTDC/MAT-PUR/31089/2017" }, { "agency": "Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia (FCT)", "grant_number": "IF/0998/2015" }, { "agency": "Ministry of Education, Science and Technological Development (Serbia)" }, { "agency": "Science Fund (Serbia)", "grant_number": "7749891" }, { "agency": "Foundation for Polish Science" }, { "agency": "European Regional Development Fund", "grant_number": "POIR.04.04.00-00-5C55/17-00" }, { "agency": "Knut and Alice Wallenberg Foundation", "grant_number": "KAW2020.0307" }, { "agency": "Swedish Research Council", "grant_number": "VR2020-04535" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "NSF", "grant_number": "DMS-1664227" } ] }, "doi": "10.1016/j.geomphys.2022.104520", "resource_type": "article", "pub_year": "2022", "author_list": "Ekholm, Tobias; Gruen, Angus; et el." }, { "id": "https://authors.library.caltech.edu/records/5p7hb-96a37", "eprint_id": 106024, "eprint_status": "archive", "datestamp": "2023-08-20 06:04:33", "lastmod": "2023-10-20 23:00:04", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Park-Sunghyuk", "name": { "family": "Park", "given": "Sunghyuk" }, "orcid": "0000-0002-6132-0871" }, { "id": "Putrov-Pavel", "name": { "family": "Putrov", "given": "Pavel" }, "orcid": "0000-0002-7207-4688" } ] }, "title": "Cobordism Invariants from BPS q-Series", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2021 Springer Nature Switzerland AG. \n\nReceived 16 February 2021; Accepted 15 July 2021; Published 29 July 2021. \n\nWe are especially grateful to Francesca Ferrari, Ciprian Manolescu, and Yi Ni for their help and insightful comments. It is also a pleasure to thank Rob Kirby and Paul Melvin for stimulating discussions and inspiration at the triple-header birthday conference \"Topology in Dimensions 3, 3.5 and 4\" in Berkeley (June, 2018). We also thank Cumrun Vafa for encouragement and comments. The work of S.G. is supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632, and by the National Science Foundation under Grant No. NSF DMS 1664227. The research of S.P. is supported by Kwanjeong Educational Foundation.\n\nSubmitted - 2009.11874.pdf
", "abstract": "Many BPS partition functions depend on a choice of additional structure: fluxes, Spin or Spin^c structures, etc. In a context where the BPS-generating series depends on a choice of Spin^c structure, we show how different limits with respect to the expansion variable q and different ways of summing over Spin^c structures produce different invariants of homology cobordisms out of the BPS q-series.", "date": "2021-12", "date_type": "published", "publication": "Annales Henri Poincar\u00e9", "volume": "22", "number": "12", "publisher": "Springer", "pagerange": "4173-4203", "id_number": "CaltechAUTHORS:20201013-115124820", "issn": "1424-0637", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20201013-115124820", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "NSF", "grant_number": "DMS-1664227" }, { "agency": "Kwanjeong Educational Foundation" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" } ] }, "doi": "10.1007/s00023-021-01089-2", "primary_object": { "basename": "2009.11874.pdf", "url": "https://authors.library.caltech.edu/records/5p7hb-96a37/files/2009.11874.pdf" }, "resource_type": "article", "pub_year": "2021", "author_list": "Gukov, Sergei; Park, Sunghyuk; et el." }, { "id": "https://authors.library.caltech.edu/records/bek1j-4v298", "eprint_id": 109623, "eprint_status": "archive", "datestamp": "2023-08-22 11:21:06", "lastmod": "2023-10-23 18:05:16", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Hsin-Po-Shen", "name": { "family": "Hsin", "given": "Po-Shen" }, "orcid": "0000-0002-4764-1476" }, { "id": "Nakajima-Hiraku", "name": { "family": "Nakajima", "given": "Hiraku" }, "orcid": "0000-0002-6060-758X" }, { "id": "Park-Sunghyuk", "name": { "family": "Park", "given": "Sunghyuk" }, "orcid": "0000-0002-6132-0871" }, { "id": "Pei-Du", "name": { "family": "Pei", "given": "Du" }, "orcid": "0000-0001-5587-6905" }, { "id": "Sopenko-Nikita", "name": { "family": "Sopenko", "given": "Nikita" }, "orcid": "0000-0002-8479-1924" } ] }, "title": "Rozansky-Witten geometry of Coulomb branches and logarithmic knot invariants", "ispublished": "pub", "full_text_status": "public", "keywords": "Equivariant index formula; Verlinde formula; Rozansky-Witten theory; ADO invariants", "note": "\u00a9 2021 Elsevier. \n\nReceived 7 February 2021, Accepted 14 June 2021, Available online 18 June 2021. \n\nIt is pleasure to thank J\u00f8rgen Andersen, Francesco Costantino, Pavel Etingof, Boris Feigin, Igor Frenkel, Azat Gainutdinov, Amihay Hanany, Anna Lachowska, Ciprian Manolescu, Jun Murakami, Mark Penney, Lev Rozansky, and Shing-Tung Yau for illuminating discussions and comments. The work of S.G. is supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632, and by the National Science Foundation under Grant No. NSF DMS 1664240. The work of P.-S.H. is supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632, and by the Simons Foundation through the Simons Investigator Award. The work of H.N. is supported in part by the World Premier International Research Center Initiative (WPI Initiative), MEXT, Japan, and by JSPS Grant Number 16H06335, 19K21828. The work of S.P. is supported by Kwanjeong Educational Foundation. The work of D.P. is supported by the Center for Mathematical Sciences and Applications at Harvard University. N.S. gratefully acknowledges the support of the Dominic Orr Graduate Fellowship at Caltech.\n\nSubmitted - 2005.05347.pdf
", "abstract": "By studying Rozansky-Witten theory with non-compact target spaces we find new connections with knot invariants whose physical interpretation was not known. This opens up several new avenues, which include a new formulation of q-series invariants of 3-manifolds in terms of affine Grassmannians and a generalization of Akutsu-Deguchi-Ohtsuki knot invariants.", "date": "2021-10", "date_type": "published", "publication": "Journal of Geometry and Physics", "volume": "168", "publisher": "Elsevier", "pagerange": "Art. No. 104311", "id_number": "CaltechAUTHORS:20210628-191053120", "issn": "0393-0440", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210628-191053120", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "NSF", "grant_number": "DMS-1664240" }, { "agency": "Simons Foundation" }, { "agency": "Ministry of Education, Culture, Sports, Science and Technology (MEXT)" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "16H06335" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "19K21828" }, { "agency": "Kwanjeong Educational Foundation" }, { "agency": "Harvard University" }, { "agency": "Dominic Orr Graduate Fellowship" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" } ] }, "doi": "10.1016/j.geomphys.2021.104311", "primary_object": { "basename": "2005.05347.pdf", "url": "https://authors.library.caltech.edu/records/bek1j-4v298/files/2005.05347.pdf" }, "resource_type": "article", "pub_year": "2021", "author_list": "Gukov, Sergei; Hsin, Po-Shen; et el." }, { "id": "https://authors.library.caltech.edu/records/0nnh3-60036", "eprint_id": 106623, "eprint_status": "archive", "datestamp": "2023-08-20 03:23:45", "lastmod": "2023-10-20 23:38:16", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Halverson-James", "name": { "family": "Halverson", "given": "James" }, "orcid": "0000-0003-0535-2622" }, { "id": "Ruehle-Fabian", "name": { "family": "Ruehle", "given": "Fabian" }, "orcid": "0000-0002-8409-9823" }, { "id": "Su\u0142kowski-Piotr", "name": { "family": "Su\u0142kowski", "given": "Piotr" }, "orcid": "0000-0002-6176-6240" } ] }, "title": "Learning to unknot", "ispublished": "pub", "full_text_status": "public", "keywords": "knot theory, string theory, machine learning, reinforcement learning", "note": "\u00a9 2021 The Author(s). Published by IOP Publishing Ltd.\nOriginal content from this work may be used under the terms of the Creative Commons Attribution 4.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. \n\nReceived 9 November 2020; Accepted 23 February 2021; Published 21 April 2021. \n\nWe thank Peter Battaglia, Kyle Cranmer, Michael Freedman, Mark Hughes, Ciprian Manolescu, Alex Radovic, Danilo Rezende, and Adam Sikora for useful discussions. The work of S.G. is supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632, and by the National Science Foundation under Grant No. NSF DMS 1664227. J.H. is supported by NSF CAREER grant PHY-1848089. The work of P.S. is supported by the TEAM programme of the Foundation for Polish Science co-financed by the European Union under the European Regional Development Fund (POIR.04.04.00-00-5C55/17-00). \n\nData availability statement: The data that support the findings of this study are available upon reasonable request from the authors.\n\nPublished - Gukov_2021_Mach._Learn.__Sci._Technol._2_025035.pdf
Submitted - 2010.16263.pdf
", "abstract": "We introduce natural language processing into the study of knot theory, as made natural by the braid word representation of knots. We study the UNKNOT problem of determining whether or not a given knot is the unknot. After describing an algorithm to randomly generate N-crossing braids and their knot closures and discussing the induced prior on the distribution of knots, we apply binary classification to the UNKNOT decision problem. We find that the Reformer and shared-QK Transformer network architectures outperform fully-connected networks, though all perform at \u227395% accuracy. Perhaps surprisingly, we find that accuracy increases with the length of the braid word, and that the networks learn a direct correlation between the confidence of their predictions and the degree of the Jones polynomial. Finally, we utilize reinforcement learning (RL) to find sequences of Markov moves and braid relations that simplify knots and can identify unknots by explicitly giving the sequence of unknotting actions. Trust region policy optimization (TRPO) performs consistently well, reducing \u227380% of the unknots with up to 96 crossings we tested to the empty braid word, and thoroughly outperformed other RL algorithms and random walkers. Studying these actions, we find that braid relations are more useful in simplifying to the unknot than one of the Markov moves.", "date": "2021-06", "date_type": "published", "publication": "Machine Learning: Science and Technology", "volume": "2", "number": "2", "publisher": "IOP Publishing", "pagerange": "Art. No. 025035", "id_number": "CaltechAUTHORS:20201111-131628016", "issn": "2632-2153", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20201111-131628016", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "NSF", "grant_number": "DMS-1664227" }, { "agency": "NSF", "grant_number": "PHY-1848089" }, { "agency": "Foundation for Polish Science" }, { "agency": "European Regional Development Fund", "grant_number": "POIR.04.04.00-00-5C55/17-00" } ] }, "other_numbering_system": { "items": [ { "id": "2020-046", "name": "CALT-TH" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" } ] }, "doi": "10.1088/2632-2153/abe91f", "primary_object": { "basename": "2010.16263.pdf", "url": "https://authors.library.caltech.edu/records/0nnh3-60036/files/2010.16263.pdf" }, "related_objects": [ { "basename": "Gukov_2021_Mach._Learn.__Sci._Technol._2_025035.pdf", "url": "https://authors.library.caltech.edu/records/0nnh3-60036/files/Gukov_2021_Mach._Learn.__Sci._Technol._2_025035.pdf" } ], "resource_type": "article", "pub_year": "2021", "author_list": "Gukov, Sergei; Halverson, James; et el." }, { "id": "https://authors.library.caltech.edu/records/tbg1f-ft873", "eprint_id": 99245, "eprint_status": "archive", "datestamp": "2023-08-20 02:52:31", "lastmod": "2023-10-18 18:10:13", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Pei-Du", "name": { "family": "Pei", "given": "Du" }, "orcid": "0000-0001-5587-6905" }, { "id": "Putrov-Pavel", "name": { "family": "Putrov", "given": "Pavel" } }, { "id": "Vafa-Cumrun", "name": { "family": "Vafa", "given": "Cumrun" } } ] }, "title": "4-manifolds and topological modular forms", "ispublished": "pub", "full_text_status": "public", "keywords": "Conformal Field Theory, Anomalies in Field and String Theories, Differential and Algebraic Geometry, Topological Field Theories", "note": "\u00a9 2021 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. \n\nArticle funded by SCOAP3. \n\nReceived: December 9, 2020; Accepted: April 5, 2021; Published: May 11, 2021. \n\nWe would like to thank Ali Daemi, Mike Freedman, Mike Hopkins, Anton Kapustin, Ciprian Manolescu, Kantaro Ohmori, Shlomo Razamat, Peter Teichner, Edward Witten, Ida Zadeh, Gabi Zafrir, and Michele del Zotto for fruitful discussions. We especially would like to thank Peter Teichner for extensive discusions on topological modular forms and Edward Witten for his suggestion to view the 4-manifold invariants we obtain from 6d (1, 0) theories as defining a class in TMF. The work of S.G. is supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632, and by the National Science Foundation under Grant No. NSF DMS 1664240. The work of D.P. is supported by the Walter Burke Institute for Theoretical Physics, the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632, and in part by the center of excellence grant \"Center for Quantum Geometry of Moduli Space\" from the Danish National Research Foundation (DNRF95). P.P. gratefully acknowledges the support from Marvin L. Goldberger Fellowship and the DOE Grant 51 DE-SC0009988 during his affiliation with IAS. The work of C.V. is supported in part by NSF grant PHY-1067976. We would like to thank the hospitality of Simons Center for Geometry and Physics, Kavli Institute for Theoretical Physics, International Center for Theoretical Physics, and Max Planck Institute for Mathematics where parts of this work were done.\n\nPublished - Gukov2021_Article_4-manifoldsAndTopologicalModul.pdf
Submitted - 1811.07884.pdf
", "abstract": "We build a connection between topology of smooth 4-manifolds and the theory of topological modular forms by considering topologically twisted compactification of 6d (1, 0) theories on 4-manifolds with flavor symmetry backgrounds. The effective 2d theory has (0, 1) supersymmetry and, possibly, a residual flavor symmetry. The equivariant topological Witten genus of this 2d theory then produces a new invariant of the 4-manifold equipped with a principle bundle, valued in the ring of equivariant weakly holomorphic (topological) modular forms. We describe basic properties of this map and present a few simple examples. As a byproduct, we obtain some new results on 't Hooft anomalies of 6d (1, 0) theories and a better understanding of the relation between 2d (0, 1) theories and TMF spectra.", "date": "2021-05", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2021", "number": "5", "publisher": "Springer", "pagerange": "Art. No. 84", "id_number": "CaltechAUTHORS:20191014-080803922", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20191014-080803922", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "NSF", "grant_number": "DMS-1664240" }, { "agency": "Walter Burke Institute for Theoretical Physics, Caltech" }, { "agency": "Danish National Research Foundation", "grant_number": "DNRF95" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0009988" }, { "agency": "NSF", "grant_number": "PHY-1067976" }, { "agency": "SCOAP3" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" } ] }, "doi": "10.1007/JHEP05(2021)084", "primary_object": { "basename": "1811.07884.pdf", "url": "https://authors.library.caltech.edu/records/tbg1f-ft873/files/1811.07884.pdf" }, "related_objects": [ { "basename": "Gukov2021_Article_4-manifoldsAndTopologicalModul.pdf", "url": "https://authors.library.caltech.edu/records/tbg1f-ft873/files/Gukov2021_Article_4-manifoldsAndTopologicalModul.pdf" } ], "resource_type": "article", "pub_year": "2021", "author_list": "Gukov, Sergei; Pei, Du; et el." }, { "id": "https://authors.library.caltech.edu/records/b9ndr-ppw42", "eprint_id": 106619, "eprint_status": "archive", "datestamp": "2023-08-22 09:24:06", "lastmod": "2023-10-20 23:38:03", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Hsin-Po-Shen", "name": { "family": "Hsin", "given": "Po-Shen" }, "orcid": "0000-0002-4764-1476" }, { "id": "Pei-Du", "name": { "family": "Pei", "given": "Du" }, "orcid": "0000-0001-5587-6905" } ] }, "title": "Generalized global symmetries of T[M] theories. Part I", "ispublished": "pub", "full_text_status": "public", "keywords": "Anomalies in Field and String Theories; Field Theories in Higher Dimensions; Global Symmetries; Topological Field Theories", "note": "\u00a9 2021 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. \n\nArticle funded by SCOAP3. \n\nReceived: November 12, 2020; Revised: March 21, 2021; Accepted: March 22, 2021; Published: April 23, 2021. \n\nWe would like to thank Dan Freed, Anton Kapustin, Pavel Putrov, Nathan Seiberg, Cumrun Vafa, Juven Wang, Edward Witten, and Shing-Tung Yau for illuminating discussions and comments. We would like to especially thank Nikita Sopenko for participation at the early stage of this project. The work of S.G. is supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632, and by the National Science Foundation under Grant No. NSF DMS 1664227. The work of P.-S. H. is supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632, and by the Simons Foundation through the Simons Investigator Award. The work of D.P. is supported by the Center for Mathematical Sciences and Applications at Harvard University, and by an NSF grant DMS-0932078, administered by the Mathematical Sciences Research Institute while the author was in residence at MSRI for the program \"Holomorphic differentials in mathematics and physics\" during the Fall of 2019.\n\nPublished - Gukov2021_Article_GeneralizedGlobalSymmetriesOfT.pdf
Accepted Version - 2010.15890.pdf
", "abstract": "We study reductions of 6d theories on a d-dimensional manifold M_d, focusing on the interplay between symmetries, anomalies, and dynamics of the resulting (6 \u2212 d)-dimensional theory T[M_d]. We refine and generalize the notion of \"polarization\" to polarization on M_d, which serves to fix the spectrum of local and extended operators in T[M_d]. Another important feature of theories T[M_d] is that they often possess higher-group symmetries, such as 2-group and 3-group symmetries. We study the origin of such symmetries as well as physical implications including symmetry breaking and symmetry enhancement in the renormalization group flow. To better probe the IR physics, we also investigate the 't Hooft anomaly of 5d Chern-Simons matter theories. The present paper focuses on developing the general framework as well as the special case of d = 0 and 1, while an upcoming paper will discuss the case of d = 2, 3 and 4.", "date": "2021-04", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2021", "number": "4", "publisher": "Springer", "pagerange": "Art. No. 232", "id_number": "CaltechAUTHORS:20201111-130432310", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20201111-130432310", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "NSF", "grant_number": "DMS-1664227" }, { "agency": "Simons Foundation" }, { "agency": "NSF", "grant_number": "DMS-0932078" }, { "agency": "SCOAP3" } ] }, "other_numbering_system": { "items": [ { "id": "2020-045", "name": "CALT-TH" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" } ] }, "doi": "10.1007/JHEP04(2021)232", "primary_object": { "basename": "2010.15890.pdf", "url": "https://authors.library.caltech.edu/records/b9ndr-ppw42/files/2010.15890.pdf" }, "related_objects": [ { "basename": "Gukov2021_Article_GeneralizedGlobalSymmetriesOfT.pdf", "url": "https://authors.library.caltech.edu/records/b9ndr-ppw42/files/Gukov2021_Article_GeneralizedGlobalSymmetriesOfT.pdf" } ], "resource_type": "article", "pub_year": "2021", "author_list": "Gukov, Sergei; Hsin, Po-Shen; et el." }, { "id": "https://authors.library.caltech.edu/records/44cpt-j4p70", "eprint_id": 108717, "eprint_status": "archive", "datestamp": "2023-08-20 02:18:57", "lastmod": "2023-10-20 23:08:54", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Manolescu-Ciprian", "name": { "family": "Manolescu", "given": "Ciprian" } } ] }, "title": "A two-variable series for knot complements", "ispublished": "pub", "full_text_status": "public", "keywords": "WRT invariants, BPS states, Dehn surgery, resurgence, colored Jones polynomial", "note": "\u00a9 2021 European Mathematical Society. Published by EMS Press. This work is licensed under a CC BY 4.0 license. \n\nReceived June 7, 2019. Published online: 2021-03-15. \n\nSergei Gukovwas supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632, and by the National Science Foundation under Grant No. DMS 1664240. \n\nCiprian Manolescu was supported by the National Science Foundation under Grant No. DMS-1708320.\n\nPublished - QT-2021-012-001-01.pdf
Accepted Version - 1904.06057.pdf
", "abstract": "The physical 3d N=2 theory T[Y] was previously used to predict the existence of some 3-manifold invariants Za(q) that take the form of power series with integer coefficients, converging in the unit disk. Their radial limits at the roots of unity should recover the Witten\u2013Reshetikhin\u2013Turaev invariants. In this paper we discuss how, for complements of knots in S\u00b3, the analogue of the invariants Za(q) should be a two-variable series F_K(x,q) obtained by parametric resurgence from the asymptotic expansion of the colored Jones polynomial. The terms in this series should satisfy a recurrence given by the quantum A-polynomial. Furthermore, there is a formula that relates F_K(x,q) to the invariants Za(q) for Dehn surgeries on the knot. We provide explicit calculations of F_K(x,q) in the case of knots given by negative definite plumbings with an unframed vertex, such as torus knots. We also find numerically the first terms in the series for the figure-eight knot, up to any desired order, and use this to understand Za(q) for some hyperbolic 3-manifolds.", "date": "2021-03-15", "date_type": "published", "publication": "Quantum Topology", "volume": "12", "number": "1", "publisher": "European Mathematical Society", "pagerange": "1-109", "id_number": "CaltechAUTHORS:20210413-133913817", "issn": "1663-487X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210413-133913817", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "NSF", "grant_number": "DMS-1664240" }, { "agency": "NSF", "grant_number": "DMS-1708320" } ] }, "doi": "10.4171/QT/145", "primary_object": { "basename": "1904.06057.pdf", "url": "https://authors.library.caltech.edu/records/44cpt-j4p70/files/1904.06057.pdf" }, "related_objects": [ { "basename": "QT-2021-012-001-01.pdf", "url": "https://authors.library.caltech.edu/records/44cpt-j4p70/files/QT-2021-012-001-01.pdf" } ], "resource_type": "article", "pub_year": "2021", "author_list": "Gukov, Sergei and Manolescu, Ciprian" }, { "id": "https://authors.library.caltech.edu/records/6ky39-9jb76", "eprint_id": 106591, "eprint_status": "archive", "datestamp": "2023-08-20 00:07:50", "lastmod": "2023-10-20 23:36:47", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Franco-Sebasti\u00e1n", "name": { "family": "Franco", "given": "Sebasti\u00e1n" } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Lee-Sangmin", "name": { "family": "Lee", "given": "Sangmin" } }, { "id": "Seong-Rak-Kyeong", "name": { "family": "Seong", "given": "Rak-Kyeong" } }, { "id": "Sparks-James", "name": { "family": "Sparks", "given": "James" } } ] }, "title": "\"Lagrangian disks\" in M-theory", "ispublished": "pub", "full_text_status": "public", "keywords": "Brane Dynamics in Gauge Theories, D-branes, M-Theory, Supersymmetric Gauge Theory", "note": "\u00a9 2020 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.\nArticle funded by SCOAP3.\n\nReceived: April 26, 2020; Revised: September 11, 2020; Accepted: September 27, 2020; Published: November 10, 2020. \n\nIt is pleasure to thank Robert Bryant, Lorenzo Foscolo, Sheldon Katz, Rafe Mazzeo, Jeffrey Meier, Grigory Mikhalkin, and Nathan Seiberg for useful discussions. The work of S.F. is supported by the National Science Foundation grant PHY-1820721. The work of S.G. is supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632, and by the National Science Foundation under Grant No. NSF DMS 1664240. The work of S.L. is supported by Samsung Science and Technology Foundation under Project Number SSTF-BA1402-08.\n\nPublished - 2020_Article_.pdf
Submitted - 1910.01645.pdf
", "abstract": "While the study of bordered (pseudo-)holomorphic curves with boundary on Lagrangian submanifolds has a long history, a similar problem that involves (special) Lagrangian submanifolds with boundary on complex surfaces appears to be largely overlooked in both physics and math literature. We relate this problem to geometry of coassociative submanifolds in G\u2082 holonomy spaces and to Spin(7) metrics on 8-manifolds with T\u00b2 fibrations. As an application to physics, we propose a large class of brane models in type IIA string theory that generalize brane brick models on the one hand and 2d theories T[M\u2084] on the other.", "date": "2020-11", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2020", "number": "11", "publisher": "Springer", "pagerange": "Art. No. 33", "id_number": "CaltechAUTHORS:20201110-123837447", "issn": "1029-8479", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20201110-123837447", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-1820721" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "NSF", "grant_number": "DMS-1664240" }, { "agency": "Samsung Science and Technology Foundation", "grant_number": "SSTF-BA1402-08" }, { "agency": "SCOAP3" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" } ] }, "doi": "10.1007/jhep11(2020)033", "primary_object": { "basename": "1910.01645.pdf", "url": "https://authors.library.caltech.edu/records/6ky39-9jb76/files/1910.01645.pdf" }, "related_objects": [ { "basename": "2020_Article_.pdf", "url": "https://authors.library.caltech.edu/records/6ky39-9jb76/files/2020_Article_.pdf" } ], "resource_type": "article", "pub_year": "2020", "author_list": "Franco, Sebasti\u00e1n; Gukov, Sergei; et el." }, { "id": "https://authors.library.caltech.edu/records/bkvxa-xz107", "eprint_id": 89664, "eprint_status": "archive", "datestamp": "2023-08-19 23:32:17", "lastmod": "2023-10-18 22:54:29", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Dedushenko-M", "name": { "family": "Dedushenko", "given": "Mykola" }, "orcid": "0000-0002-9273-7602" }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Nakajima-Hiraku", "name": { "family": "Nakajima", "given": "Hiraku" } }, { "id": "Pei-Du", "name": { "family": "Pei", "given": "Du" }, "orcid": "0000-0001-5587-6905" }, { "id": "Ye-Ke", "name": { "family": "Ye", "given": "Ke" }, "orcid": "0000-0002-2978-2013" } ] }, "title": "3d TQFTs from Argyres\u2013Douglas theories", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2020 IOP Publishing Ltd. \n\nReceived 24 February 2020; Revised 27 August 2020; Accepted 2 September 2020; Published 8 October 2020. \n\nWe thank J E Andersen, B Feigin, L Fredrickson, K Maruyoshi and N Nekrasov for interesting discussions. The work of MD, SG, DP and KY was supported by the Walter Burke Institute for Theoretical Physics and the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632. The work of MD was also supported by the Sherman Fairchild Foundation. The work of SG was also supported by the National Science Foundation under Grant No. NSF DMS 1664240. The work of DP was also supported in part by the center of excellence grant 'Center for Quantum Geometry of Moduli Space' from the Danish National Research Foundation (DNRF95) and the Center for Mathematical Sciences and Applications. The research of HN was supported in part by the World Premier International Research Center Initiative (WPI Initiative), MEXT, Japan, and by JSPS Grant No. 16H06335.\n\nSubmitted - 1809.04638.pdf
", "abstract": "We construct a new class of three-dimensional topological quantum field theories (3d TQFTs) by considering generalized Argyres\u2013Douglas theories on S\u00b9 \u00d7 M\u2083 with a non-trivial holonomy of a discrete global symmetry along the S\u00b9. For the minimal choice of the holonomy, the resulting 3d TQFTs are non-unitary and semisimple, thus distinguishing themselves from theories of Chern\u2013Simons and Rozansky\u2013Witten types respectively. Changing the holonomy performs a Galois transformation on the TQFT, which can sometimes give rise to more familiar unitary theories such as the (G\u2082)\u2081 and (F\u2084)\u2081 Chern\u2013Simons theories. Our construction is based on an intriguing relation between topologically twisted partition functions, wild Hitchin characters, and chiral algebras which, when combined together, relate Coulomb branch and Higgs branch data of the same 4d N = 2 theory. We test our proposal by applying localization techniques to the conjectural N = 1 UV Lagrangian descriptions of the (A\u2081, A\u2082), (A\u2081, A\u2083) and (A\u2081, D\u2083) theories.", "date": "2020-10", "date_type": "published", "publication": "Journal of Physics A: Mathematical and General", "volume": "53", "number": "43", "publisher": "IOP", "pagerange": "Art. No. 43LT01", "id_number": "CaltechAUTHORS:20180915-165620259", "issn": "0305-4470", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180915-165620259", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Walter Burke Institute for Theoretical Physics, Caltech" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "Sherman Fairchild Foundation" }, { "agency": "NSF", "grant_number": "DMS-1664240" }, { "agency": "Danish National Research Foundation", "grant_number": "DNRF95" }, { "agency": "Ministry of Education, Culture, Sports, Science and Technology (MEXT)" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "16H06335" } ] }, "other_numbering_system": { "items": [ { "id": "2018-033", "name": "CALT-TH" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" } ] }, "doi": "10.1088/1751-8121/abb481", "primary_object": { "basename": "1809.04638.pdf", "url": "https://authors.library.caltech.edu/records/bkvxa-xz107/files/1809.04638.pdf" }, "resource_type": "article", "pub_year": "2020", "author_list": "Dedushenko, Mykola; Gukov, Sergei; et el." }, { "id": "https://authors.library.caltech.edu/records/cf8rb-yre64", "eprint_id": 105543, "eprint_status": "archive", "datestamp": "2023-08-19 23:12:11", "lastmod": "2023-10-20 22:06:32", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Chun-Sungbong", "name": { "family": "Chun", "given": "Sungbong" } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Park-Sunghyuk", "name": { "family": "Park", "given": "Sunghyuk" }, "orcid": "0000-0002-6132-0871" }, { "id": "Sopenko-N", "name": { "family": "Sopenko", "given": "Nikita" } } ] }, "title": "3d-3d correspondence for mapping tori", "ispublished": "pub", "full_text_status": "public", "keywords": "Conformal Field Models in String Theory, Supersymmetric Effective Theories, Topological Field Theories", "note": "\u00a9 2020 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. \n\nReceived: June 29, 2020. Accepted: August 25, 2020. Published: September 23, 2020. \n\nArticle funded by SCOAP3. \n\nIt is pleasure to thank Ian Agol, Francesco Benini, Miranda Cheng, Francesca Ferrari, Michael Freedman, Sarah Harrison, Jeremy Lovejoy, Ciprian Manolescu, Satoshi Nawata, Du Pei, Pavel Putrov, Larry Rolen, Nathan Seiberg, Cumrun Vafa, and Christian Zickert for help and suggestions. The work of S.C. was supported by the US Department of Energy under grant DE-SC0010008. The work of S.G. is supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632, and by the National Science Foundation under Grant No. NSF DMS 1664240. The work of S.P. is supported by Kwanjeong Educational Foundation. N.S. gratefully acknowledges the support of the Dominic Orr Graduate Fellowship at Caltech.\n\nPublished - Chun2020_Article_3d-3dCorrespondenceForMappingT.pdf
Accepted Version - 1911.08456.pdf
", "abstract": "One of the main challenges in 3d-3d correspondence is that no existent approach offers a complete description of 3d N = 2 SCFT T [M\u2083] \u2014 or, rather, a \"collection of SCFTs\" as we refer to it in the paper \u2014 for all types of 3-manifolds that include, for example, a 3-torus, Brieskorn spheres, and hyperbolic surgeries on knots. The goal of this paper is to overcome this challenge by a more systematic study of 3d-3d correspondence that, first of all, does not rely heavily on any geometric structure on M\u2083 and, secondly, is not limited to a particular supersymmetric partition function of T [M\u2083]. In particular, we propose to describe such \"collection of SCFTs\" in terms of 3d N = 2 gauge theories with \"non-linear matter\" fields valued in complex group manifolds. As a result, we are able to recover familiar 3-manifold invariants, such as Turaev torsion and WRT invariants, from twisted indices and half-indices of T [M\u2083], and propose new tools to compute more recent q-series invariants \u1e90 (M\u2083) in the case of manifolds with b\u2081 > 0. Although we use genus-1 mapping tori as our \"case study,\" many results and techniques readily apply to more general 3-manifolds, as we illustrate throughout the paper.", "date": "2020-09", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2020", "number": "9", "publisher": "Springer", "pagerange": "Art. No. 152", "id_number": "CaltechAUTHORS:20200925-091915393", "issn": "1029-8479", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200925-091915393", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "SCOAP3" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0010008" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "NSF", "grant_number": "DMS-1664240" }, { "agency": "Kwanjeong Educational Foundation" }, { "agency": "Dominic Orr Graduate Fellowship" } ] }, "other_numbering_system": { "items": [ { "id": "2019-048", "name": "CALT-TH" } ] }, "doi": "10.1007/jhep09(2020)152", "primary_object": { "basename": "1911.08456.pdf", "url": "https://authors.library.caltech.edu/records/cf8rb-yre64/files/1911.08456.pdf" }, "related_objects": [ { "basename": "Chun2020_Article_3d-3dCorrespondenceForMappingT.pdf", "url": "https://authors.library.caltech.edu/records/cf8rb-yre64/files/Chun2020_Article_3d-3dCorrespondenceForMappingT.pdf" } ], "resource_type": "article", "pub_year": "2020", "author_list": "Chun, Sungbong; Gukov, Sergei; et el." }, { "id": "https://authors.library.caltech.edu/records/2kwzk-b1v64", "eprint_id": 102500, "eprint_status": "archive", "datestamp": "2023-08-19 20:45:03", "lastmod": "2023-10-20 00:15:57", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Pei-Du", "name": { "family": "Pei", "given": "Du" }, "orcid": "0000-0001-5587-6905" }, { "id": "Putrov-P", "name": { "family": "Putrov", "given": "Pavel" } } ] }, "title": "Trialities of minimally supersymmetric 2d gauge theories", "ispublished": "pub", "full_text_status": "public", "keywords": "Anomalies in Field and String Theories, Supersymmetric Gauge Theory,\nSupersymmetry and Duality, Sigma Models", "note": "\u00a9 2020 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. \n\nArticle funded by SCOAP3. \n\nReceived: January 27, 2020; Accepted: March 25, 2020; Published: April 14, 2020. \n\nWe would like to thank Francesco Benini, Mykola Dedushenko, Shiraz Minwalla, Cumrun Vafa, Edward Witten for fruitful discussions. The work of S.G. is supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632, and by the National Science Foundation under Grant No. NSF DMS 1664240. The work of D.P. is supported by NSF Grant DMS-1440140 while in residence at the Mathematical Sciences Research Institute in Berkeley, California during the Fall 2019 semester, and by the center of excellence grant \"Center for Quantum Geometry of Moduli Space\" from the Danish National Research Foundation (DNRF95).\n\nPublished - Gukov2020_Article_TrialitiesOfMinimallySupersymm.pdf
Submitted - 1910.13455.pdf
", "abstract": "We study dynamics of two-dimensional N = (0, 1) supersymmetric gauge theories. In particular, we propose that there is an infrared triality between certain triples of theories with orthogonal and symplectic gauge groups. The proposal is supported by matching of anomalies and elliptic genera. This triality can be viewed as a (0, 1) counterpart of the (0, 2) triality proposed earlier by two of the authors and A. Gadde. We also describe the relation between global anomalies in gauge theoretic and sigma-model descriptions, filling in a gap in the present literature.", "date": "2020-04", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2020", "number": "4", "publisher": "Springer", "pagerange": "Art. No. 079", "id_number": "CaltechAUTHORS:20200413-094559729", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200413-094559729", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "NSF", "grant_number": "DMS-1664240" }, { "agency": "NSF", "grant_number": "DMS-1440140" }, { "agency": "Danish National Research Foundation", "grant_number": "DNRF95" }, { "agency": "SCOAP3" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" } ] }, "doi": "10.1007/JHEP04(2020)079", "primary_object": { "basename": "1910.13455.pdf", "url": "https://authors.library.caltech.edu/records/2kwzk-b1v64/files/1910.13455.pdf" }, "related_objects": [ { "basename": "Gukov2020_Article_TrialitiesOfMinimallySupersymm.pdf", "url": "https://authors.library.caltech.edu/records/2kwzk-b1v64/files/Gukov2020_Article_TrialitiesOfMinimallySupersymm.pdf" } ], "resource_type": "article", "pub_year": "2020", "author_list": "Gukov, Sergei; Pei, Du; et el." }, { "id": "https://authors.library.caltech.edu/records/agh1q-xw932", "eprint_id": 73923, "eprint_status": "archive", "datestamp": "2023-08-22 03:43:44", "lastmod": "2023-10-24 21:06:54", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Pei-Du", "name": { "family": "Pei", "given": "Du" }, "orcid": "0000-0001-5587-6905" }, { "id": "Putrov-P", "name": { "family": "Putrov", "given": "Pavel" } }, { "id": "Vafa-C", "name": { "family": "Vafa", "given": "Cumrun" } } ] }, "title": "BPS spectra and 3-manifold invariants", "ispublished": "pub", "full_text_status": "public", "keywords": "BPS spectrum; 3-manifold; invariant; knot", "note": "\u00a9 2020 World Scientific Publishing Company. \n\nReceived 7 January 2020; Accepted 13 January 2020; Published 17 March 2020. \n\nWe would like to thank J. E. Andersen, M. Aganagic, F. Benini, C. Cordova, A.Gadde, E. Gorsky,K. Hori,H. Kim, S. Nawata,M. Romo, S. Shakirov, L. Rozansky and K. Ye for useful comments and discussions. The work of S.G. and D.P. is supported in part by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632. In addition, the work of D.P. is supported by the center of excellence grant \"Center for Quantum Geometry of Moduli Space\" from the Danish National Research Foundation (DNRF95). P.P. gratefully acknowledges the support from Marvin L. Goldberger Fellowship and the DOE Grant DE-SC0009988. The research of C.V. is supported in part by NSF grant PHY-1067976. This work was performed in part (by P.P.) at Aspen Center for Physics which is supported by National Science Foundation grant PHY-1066293. The authors would like to thank Simons Center for Geometry and Physics and the organisers of the Simons Summer Workshop 2016, where the work on the project has begun, for generous hospitality.\n\nSubmitted - 1701.06567v1.pdf
", "abstract": "We provide a physical definition of new homological invariants H_a(M\u2083) of 3-manifolds (possibly, with knots) labeled by abelian flat connections. The physical system in question involves a 6d fivebrane theory on M\u2083 times a 2-disk, D\u00b2, whose Hilbert space of BPS states plays the role of a basic building block in categorification of various partition functions of 3d N=2 theory T[M\u2083]: D\u00b2\u00d7S\u00b9 half-index, S\u00b2\u00d7S\u00b9 superconformal index, and S\u00b2\u00d7S\u00b9 topologically twisted index. The first partition function is labeled by a choice of boundary condition and provides a refinement of Chern\u2013Simons (WRT) invariant. A linear combination of them in the unrefined limit gives the analytically continued WRT invariant of M\u2083. The last two can be factorized into the product of half-indices. We show how this works explicitly for many examples, including Lens spaces, circle fibrations over Riemann surfaces, and plumbed 3-manifolds.", "date": "2020-02", "date_type": "published", "publication": "Journal of Knot Theory and its Ramifications", "volume": "29", "number": "2", "publisher": "World Scientific Publishing", "pagerange": "Art. No. 2040003", "id_number": "CaltechAUTHORS:20170201-100930550", "issn": "0218-2165", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170201-100930550", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "Danish National Research Foundation", "grant_number": "DNRF95" }, { "agency": "Marvin L. Goldberger Fellowship" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0009988" }, { "agency": "NSF", "grant_number": "PHY-1067976" }, { "agency": "NSF", "grant_number": "PHY-1066293" } ] }, "other_numbering_system": { "items": [ { "id": "2016-039", "name": "CALT-TH" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" } ] }, "doi": "10.1142/S0218216520400039", "primary_object": { "basename": "1701.06567v1.pdf", "url": "https://authors.library.caltech.edu/records/agh1q-xw932/files/1701.06567v1.pdf" }, "resource_type": "article", "pub_year": "2020", "author_list": "Gukov, Sergei; Pei, Du; et el." }, { "id": "https://authors.library.caltech.edu/records/dz2fj-0rp70", "eprint_id": 100543, "eprint_status": "archive", "datestamp": "2023-08-19 19:22:47", "lastmod": "2023-10-18 21:00:19", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Feigin-Boris", "name": { "family": "Feigin", "given": "Boris" } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" } ] }, "title": "VOA[M\u2084]", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2020 Published under license by AIP Publishing. \n\nSubmitted: 15 April 2019; Accepted: 5 November 2019; Published Online: 6 January 2020. \n\nThis paper is part of the Special Collection: XIXth International Congress on Mathematical Physics. \n\nWe would like to thank A. Braverman, K. Costello, T. Creutzig, J. Fuchs, A. Gadde, J. Meier, H. Nakajima, N. Paquette, P. Putrov, M. Rapcak, C. Schweigert, J. Teschner, R. Thomas, and E. Witten for valuable discussions and inspiration and F. Ferrari and S. Lee for comments on the manuscript. We also wish to thank the anonymous referee for very useful feedback and many insightful comments. The work of B.F. has been funded by the Russian Academic Excellence Project No. 5-100. The research of B.F. has also been supported by the Russian Science Foundation, Grant Project No. 16-11-10316. The work of S.G. was supported in part by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632, and in part by the National Science Foundation under Grant No. NSF DMS 1664240.\n\nPublished - 1.5100059.pdf
", "abstract": "We take a peek at a general program that associates vertex (or chiral) algebras to smooth 4-manifolds in such a way that operations on algebras mirror gluing operations on 4-manifolds and, furthermore, equivalent constructions of 4-manifolds give rise to equivalences (dualities) of the corresponding algebras.", "date": "2020-01", "date_type": "published", "publication": "Journal of Mathematical Physics", "volume": "61", "number": "1", "publisher": "American Institute of Physics", "pagerange": "Art. No. 012302", "id_number": "CaltechAUTHORS:20200107-142933165", "issn": "0022-2488", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200107-142933165", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Russian Academic Excellence Project (RAEP)", "grant_number": "5-100" }, { "agency": "Russian Science Foundation", "grant_number": "16-11-10316" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "NSF", "grant_number": "DMS-1664240" } ] }, "doi": "10.1063/1.5100059", "primary_object": { "basename": "1.5100059.pdf", "url": "https://authors.library.caltech.edu/records/dz2fj-0rp70/files/1.5100059.pdf" }, "resource_type": "article", "pub_year": "2020", "author_list": "Feigin, Boris and Gukov, Sergei" }, { "id": "https://authors.library.caltech.edu/records/crpct-nzd05", "eprint_id": 66609, "eprint_status": "archive", "datestamp": "2023-08-19 18:24:07", "lastmod": "2023-10-18 18:37:38", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gadde-A", "name": { "family": "Gadde", "given": "Abhijit" } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Putrov-P", "name": { "family": "Putrov", "given": "Pavel" } } ] }, "title": "Exact Solutions of 2d Supersymmetric Gauge Theories", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2019 The Author(s). This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. \n\nArticle funded by SCOAP3. \n\nReceived: October 20, 2019; Accepted: November 2, 2019; Published: November 29, 2019. \n\nWe would like to thank D. Gaiotto, B. Jia, I. Melnikov, V. Schomerus, and E. Sharpe for useful discussions. A.G. would also like to thank the Kavli Institute for Theoretical Physics for providing a hospitable and enjoyable work environment during the late stages of this project. The work of A.G. is supported in part by the John A. McCone fellowship and by DOE Grant DE-FG02-92-ER40701. The work of S.G. is supported in part by DOE Grant DE-FG03-92-ER40701FG-02. The work of P.P. is supported in part by the Sherman Fairchild scholarship and by NSF Grant PHY-1050729. Opinions and conclusions expressed here are those of the authors and do not necessarily reflect the views of funding agencies.\n\nPublished - Gadde2019_Article_ExactSolutionsOf2dSupersymmetr.pdf
Submitted - 1404.5314.pdf
", "abstract": "We study dynamics of two-dimensional non-abelian gauge theories with N = (0, 2) supersymmetry that include N = (0, 2) supersymmetric QCD and its generaliza- tions. In particular, we present the phase diagram of N = (0, 2) SQCD and determine its massive and low-energy spectrum. We find that the theory has no mass gap, a nearly constant distribution of massive states, and lots of massless states that in general flow to an interacting CFT. For a range of parameters where supersymmetry is not dynamically broken at low energies, we give a complete description of the low-energy physics in terms of 2d N = (0, 2) SCFTs using anomaly matching and modular invariance. Our construction provides a vast landscape of new N = (0, 2) SCFTs which, for small values of the central charge, could be used for building novel heterotic models with no moduli and, for large values of the central charge, could be dual to AdS\u2083 string vacua.", "date": "2019-11", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2019", "number": "11", "publisher": "Springer", "pagerange": "Art. No. 174", "id_number": "CaltechAUTHORS:20160503-085246813", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160503-085246813", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "John A. McCone Fellowship" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG02-92-ER40701" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701FG-02" }, { "agency": "Sherman Fairchild Foundation" }, { "agency": "NSF", "grant_number": "PHY-1050729" }, { "agency": "SCOAP3" } ] }, "doi": "10.1007/JHEP11(2019)174", "primary_object": { "basename": "1404.5314.pdf", "url": "https://authors.library.caltech.edu/records/crpct-nzd05/files/1404.5314.pdf" }, "related_objects": [ { "basename": "Gadde2019_Article_ExactSolutionsOf2dSupersymmetr.pdf", "url": "https://authors.library.caltech.edu/records/crpct-nzd05/files/Gadde2019_Article_ExactSolutionsOf2dSupersymmetr.pdf" } ], "resource_type": "article", "pub_year": "2019", "author_list": "Gadde, Abhijit; Gukov, Sergei; et el." }, { "id": "https://authors.library.caltech.edu/records/k8e0q-x5c22", "eprint_id": 99305, "eprint_status": "archive", "datestamp": "2023-08-22 02:36:57", "lastmod": "2023-10-18 18:13:17", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Cheng-Miranda-C-N", "name": { "family": "Cheng", "given": "Miranda C. N." } }, { "id": "Chun-Sungbong", "name": { "family": "Chun", "given": "Sungbong" } }, { "id": "Ferrari-F", "name": { "family": "Ferrari", "given": "Francesca" } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Harrison-S-M", "name": { "family": "Harrison", "given": "Sarah M." } } ] }, "title": "3d modularity", "ispublished": "pub", "full_text_status": "public", "keywords": "Chern-Simons Theories; Conformal Field Theory; M-Theory; Nonperturbative Effects", "note": "\u00a9 2019 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. \n\nArticle funded by SCOAP3. \n\nReceived: June 18, 2019; Accepted: August 27, 2019; Published: October 3, 2019. \n\nWe thank D. Adamovic, T. Creutzig, T. Dimofte, J. Duncan, P. Etingof, B. Feigin, D. Kazhdan, S. L\u00f6brich, C. Manolescu, D. Pei, P. Putrov, L. Rolen, C. Schweigert, C. Vafa and D. Zagier for helpful discussions. The work of M.C. is supported by ERC starting grant H2020 ERC StG #640159. S.C. and S.G. are supported by the Walter Burke Institute for Theoretical Physics, by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632, and by the National Science Foundation under Grant No. NSF DMS 1664240. The work of S.C. is also supported in part by Samsung Scholarship. The work of S.G. is also supported in part by Laboratory of Mirror Symmetry NRU HSE, RF Government grant, ag. No. 14.641.31.0001. The work of F.F. is supported in part by the MIUR-SIR grant RBSI1471GJ \"Quantum Field Theories at Strong Coupling: Exact Computations and Applications\". S.H. is supported by the National Science and Engineering Council of Canada, an FRQNT new university researchers start-up grant, and the Canada Research Chairs program. M.C. would also like to thank LPTHE, Jussieu Paris, for hospitality during the final stage of this work.\n\nPublished - Cheng2019_Article_3dModularity.pdf
Submitted - 1809.10148.pdf
", "abstract": "We find and propose an explanation for a large variety of modularity-related symmetries in problems of 3-manifold topology and physics of 3d N = 2 theories where such structures a priori are not manifest. These modular structures include: mock modular forms, SL(2,\u2124) Weil representations, quantum modular forms, non-semisimple modular tensor categories, and chiral algebras of logarithmic CFTs.", "date": "2019-10", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2019", "number": "10", "publisher": "Springer", "pagerange": "Art. No. 10", "id_number": "CaltechAUTHORS:20191016-132239333", "issn": "1029-8479", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20191016-132239333", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "European Research Council (ERC)", "grant_number": "640159" }, { "agency": "Walter Burke Institute for Theoretical Physics, Caltech" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "NSF", "grant_number": "DMS-1664240" }, { "agency": "Samsung Scholarship" }, { "agency": "Ministry of Education, Culture, Sports, Science and Technology (MEXT)", "grant_number": "14.641.31.0001" }, { "agency": "Ministero dell'Istruzione, dell'Universita e della Ricerca (MIUR)", "grant_number": "RBSI1471GJ" }, { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)" }, { "agency": "Fonds de recherche du Qu\u00e9bec - Nature et technologies (FRQNT)" }, { "agency": "Canada Research Chairs Program" }, { "agency": "SCOAP3" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" } ] }, "doi": "10.1007/jhep10(2019)010", "primary_object": { "basename": "1809.10148.pdf", "url": "https://authors.library.caltech.edu/records/k8e0q-x5c22/files/1809.10148.pdf" }, "related_objects": [ { "basename": "Cheng2019_Article_3dModularity.pdf", "url": "https://authors.library.caltech.edu/records/k8e0q-x5c22/files/Cheng2019_Article_3dModularity.pdf" } ], "resource_type": "article", "pub_year": "2019", "author_list": "Cheng, Miranda C. N.; Chun, Sungbong; et el." }, { "id": "https://authors.library.caltech.edu/records/8s609-ppc69", "eprint_id": 84212, "eprint_status": "archive", "datestamp": "2023-08-19 14:54:01", "lastmod": "2023-10-18 15:59:25", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Dedushenko-M", "name": { "family": "Dedushenko", "given": "Mykola" }, "orcid": "0000-0002-9273-7602" }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" } ] }, "title": "IR duality in 2D N = (0,2) gauge theory with noncompact dynamics", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2019 Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. \n \nFunded by SCOAP3. \n \nReceived 12 February 2018; published 14 March 2019. \n \nWe thank M. Fluder, J. Heckman, D. Jafferis, D. Kutasov, N. Nekrasov, P. Putrov, J. Song for useful discussions. This work was supported by the Walter Burke Institute for Theoretical Physics and the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632. The work of MD was also supported by the Sherman Fairchild Foundation. S. G. gratefully acknowledges support from Harvard University, where some of the research for this paper was performed during the fall 2017, as well as partial support by the National Science Foundation under Grants No. NSF PHY11-25915 and No. NSF DMS 1664240.\n\nPublished - PhysRevD.99.066005.pdf
Submitted - 1712.07659.pdf
", "abstract": "Searching for the simplest non-Abelian 2D gauge theory with N = (0,2) supersymmetry and nontrivial IR physics, we propose a new duality for SU(2) SQCD with N^f = 4 chiral flavors. The chiral algebra of this theory is found to be so(8)_(\u22122), the same as in 4D N = 2 SU(2) gauge theory with four hypermultiplets.", "date": "2019-03-15", "date_type": "published", "publication": "Physical Review D", "volume": "99", "number": "6", "publisher": "American Physical Society", "pagerange": "Art. No. 066005", "id_number": "CaltechAUTHORS:20180109-161412323", "issn": "2470-0010", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180109-161412323", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Walter Burke Institute for Theoretical Physics, Caltech" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "Sherman Fairchild Foundation" }, { "agency": "Harvard University" }, { "agency": "NSF", "grant_number": "PHY11-25915" }, { "agency": "NSF", "grant_number": "DMS-1664240" }, { "agency": "SCOAP3" } ] }, "other_numbering_system": { "items": [ { "id": "2017-072", "name": "CALT-TH" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" } ] }, "doi": "10.1103/PhysRevD.99.066005", "primary_object": { "basename": "PhysRevD.99.066005.pdf", "url": "https://authors.library.caltech.edu/records/8s609-ppc69/files/PhysRevD.99.066005.pdf" }, "related_objects": [ { "basename": "1712.07659.pdf", "url": "https://authors.library.caltech.edu/records/8s609-ppc69/files/1712.07659.pdf" } ], "resource_type": "article", "pub_year": "2019", "author_list": "Dedushenko, Mykola and Gukov, Sergei" }, { "id": "https://authors.library.caltech.edu/records/w61fx-hp647", "eprint_id": 66605, "eprint_status": "archive", "datestamp": "2023-08-19 11:23:33", "lastmod": "2023-10-18 18:37:28", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gorsky-E", "name": { "family": "Gorsky", "given": "Eugene" } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Sto\u0161i\u0107-M", "name": { "family": "Sto\u0161i\u0107", "given": "Marko" } } ] }, "title": "Quadruply-graded colored homology of knots", "ispublished": "pub", "full_text_status": "public", "keywords": "knot homology, colored HOMFLYPT invariants, BPS invariants,\ndifferentials, Lie superalgebras", "note": "\u00a9 2018 Instytut Matematyczny PAN. \n\nReceived 28 October 2014; revised 21 February 2017. Published online 3 September 2018.\n\nWe are grateful to M. Abouzaid, M. Aganagic, J. M. Baptista, M. Bershtein, I. Cherednik, K. Costello, R. Elliot, P. Etingof, A. Gorsky, K. Hikami, M. Khovanov, B. Kim, A. N. Kirillov and A. A. Kirillov Jr., I. Losev, A. Morozov, H. Nakajima, A. Negu\u00b5, N. Nekrasov, A. Oblomkov, A. Okounkov, J. Rasmussen, L. Rozansky, S. Shakirov, V. Shende, C. Vafa, O. Viro, E. Witten, and C. Woodward for useful discussions. \n\nE.G. would like to thank California Institute of Technology and Kyoto Research Institute for Mathematical Sciences for hospitality. The research of E.G. is partially supported by the NSF grant DMS-1559338, grants RFBR-10-01-678, NSh-8462.2010.1, Simons Foundation and Russian Academic Excellence Project 5-100.\nS.G. would like to thank Instituto Superior T\u00e9cnico in Lisbon and the Simons Center for Geometry and Physics at Stony Brook for hospitality during the key stages of this work. The work of S.G. is supported in part by DOE grant DE-FG03-92-ER40701FG-02 and in part by NSF grant PHY-0757647. \n\nM.S. would like to thank the California Institute of Technology for hospitality while part of this work was done. The work of S.G. and M.S. was partially supported by ERC Starting Grant no. 335739 \"Quantum fields and knot homologies\" funded by the European Research Council under the European Union Seventh Framework Programme. M.S. was also partially supported by the Portuguese Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia through the project PTDC/MAT/101503/2008, New Geometry and Topology, and\nby the Ministry of Science of Serbia, project no. 174012. Opinions and conclusions expressed here are those of the authors and do not necessarily reflect the views of the funding agencies.\n\nPublished - fm30-11-2017.pdf
Submitted - 1304.3481.pdf
", "abstract": "We conjecture the existence of four independent gradings in colored HOMFLYPT homology, and make qualitative predictions of various interesting structures and symmetries in the colored homology of arbitrary knots. We propose an explicit conjectural description for the rectangular colored homology of torus knots, and identify the new gradings in this context. While some of these structures have a natural interpretation in the physical realization of knot homologies based on counting supersymmetric configurations (BPS states, instantons, and vortices), others are completely new. They suggest new geometric and physical realizations of colored HOMFLYPT homology as the Hochschild homology of the category of branes in a Landau\u2013Ginzburg B-model or, equivalently, in the mirror A-model. Supergroups and supermanifolds are surprisingly ubiquitous in all aspects of this work.", "date": "2018-09-03", "date_type": "published", "publication": "Fundamenta Mathematicae", "volume": "243", "publisher": "Institute of Mathematics, Polish Academy of Sciences", "pagerange": "209-299", "id_number": "CaltechAUTHORS:20160503-082624275", "issn": "0016-2736", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160503-082624275", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1559338" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "RFBR-10-01-678" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "NSh-8462.2010.1" }, { "agency": "Simons Foundation" }, { "agency": "Russian Academic Excellence Project (RAEP)", "grant_number": "5-100" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701FG-02" }, { "agency": "NSF", "grant_number": "PHY-0757647" }, { "agency": "European Research Council (ERC)", "grant_number": "335739" }, { "agency": "Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia (FCT)", "grant_number": "PTDC/MAT/101503/2008" }, { "agency": "Ministry of Science (Serbia)", "grant_number": "174012" } ] }, "doi": "10.4064/fm30-11-2017", "primary_object": { "basename": "1304.3481.pdf", "url": "https://authors.library.caltech.edu/records/w61fx-hp647/files/1304.3481.pdf" }, "related_objects": [ { "basename": "fm30-11-2017.pdf", "url": "https://authors.library.caltech.edu/records/w61fx-hp647/files/fm30-11-2017.pdf" } ], "resource_type": "article", "pub_year": "2018", "author_list": "Gorsky, Eugene; Gukov, Sergei; et el." }, { "id": "https://authors.library.caltech.edu/records/ywftn-q2j47", "eprint_id": 68893, "eprint_status": "archive", "datestamp": "2023-08-19 07:31:49", "lastmod": "2023-10-20 15:51:09", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Pei-Du", "name": { "family": "Pei", "given": "Du" }, "orcid": "0000-0001-5587-6905" }, { "id": "Yan-Wenbin", "name": { "family": "Yan", "given": "Wenbin" } }, { "id": "Ye-Ke", "name": { "family": "Ye", "given": "Ke" }, "orcid": "0000-0002-2978-2013" } ] }, "title": "Equivariant Verlinde algebra from superconformal index and Argyres-Seiberg duality", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2018 Springer-Verlag GmbH Germany, part of Springer Nature. \n\nReceived: 24 July 2016; Accepted: 28 November 2017; First Online: 11 January 2018. \n\nWe thank J\u00f8rgen Ellegaard Andersen, Francesco Benini, Martin Fluder, Abhijit Gadde, Tam\u00e1s Hausel, Murat Kolo\u011flu, Pavel Putrov, Richard Wentworth, Ingmar Saberi, Jaewon Song, Andras Szenes and Masahito Yamazaki for helpful discussions related to this work. We would also like to thank the organizers of the Simons Summer Workshop 2015, where a significant portion of this project was completed. This work is funded by the DOE Grant DE-SC0011632, U.S. National Science Foundation grants DMS 1107452, 1107263, 1107367 (\"the GEAR Network\"), the Walter Burke Institute for Theoretical Physics, the center of excellence grant \"Center for Quantum Geometry of Moduli Space\" from the Danish National Research Foundation (DNRF95), and the Center of Mathematical Sciences and Applications at Harvard University.\n\nSubmitted - 1605.06528v2.pdf
Supplemental Material - 220_2017_3074_MOESM1_ESM.pdf
", "abstract": "In this paper, we show the equivalence between two seemingly distinct 2d TQFTs: one comes from the \"Coulomb branch index\" of the class SS theory T[\u03a3,G] on L(k,1)\u00d7S^1, the other is the LGLG \"equivariant Verlinde formula\", or equivalently partition function of LGCLGC complex Chern\u2013Simons theory on \u03a3\u00d7S^1. We first derive this equivalence using the M-theory geometry and show that the gauge groups appearing on the two sides are naturally G and its Langlands dual LGLG. When G is not simply-connected, we provide a recipe of computing the index of T[\u03a3,G] as summation over the indices of T[\u03a3,G] with non-trivial background 't Hooft fluxes, where G is the universal cover of G. Then we check explicitly this relation between the Coulomb index and the equivariant Verlinde formula for G=SU(2) or SO(3). In the end, as an application of this newly found relation, we consider the more general case where G is SU(N) or PSU(N) and show that equivariant Verlinde algebra can be derived using field theory via (generalized) Argyres\u2013Seiberg duality. We also attach a Mathematica notebook that can be used to compute the SU(3) equivariant Verlinde coefficients.", "date": "2018-02", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "357", "number": "3", "publisher": "Springer", "pagerange": "1215-1251", "id_number": "CaltechAUTHORS:20160707-133458529", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160707-133458529", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "NSF", "grant_number": "DMS-1107452" }, { "agency": "NSF", "grant_number": "DMS-1107263" }, { "agency": "NSF", "grant_number": "DMS-1107367" }, { "agency": "Walter Burke Institute for Theoretical Physics, Caltech" }, { "agency": "Danish National Research Foundation", "grant_number": "DNRF95" }, { "agency": "Harvard University" } ] }, "other_numbering_system": { "items": [ { "id": "2016-012", "name": "CALT-TH" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" } ] }, "doi": "10.1007/s00220-017-3074-8", "primary_object": { "basename": "1605.06528v2.pdf", "url": "https://authors.library.caltech.edu/records/ywftn-q2j47/files/1605.06528v2.pdf" }, "related_objects": [ { "basename": "220_2017_3074_MOESM1_ESM.pdf", "url": "https://authors.library.caltech.edu/records/ywftn-q2j47/files/220_2017_3074_MOESM1_ESM.pdf" } ], "resource_type": "article", "pub_year": "2018", "author_list": "Gukov, Sergei; Pei, Du; et el." }, { "id": "https://authors.library.caltech.edu/records/qr4fk-vrs74", "eprint_id": 79256, "eprint_status": "archive", "datestamp": "2023-08-19 05:47:05", "lastmod": "2023-10-26 14:44:31", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" } ] }, "title": "Trisecting non-Lagrangian theories", "ispublished": "pub", "full_text_status": "public", "keywords": "Topological Field Theories, Supersymmetry and Duality, D-branes, Topological Strings", "note": "\u00a9 2017 The Author(s). This article is distributed under the terms of the Creative Commons ttribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. \n\nArticle funded by SCOAP3. \n\nReceived: October 5, 2017; Accepted: November 6, 2017; Published: November 27, 2017. \n\nIt is pleasure to thank M. Atiyah, M. Dedushenko, T. Dumitrescu, D. Gay, A. Giveon, N. Hitchin, R. Kirby, D. Kutasov, D. L\u00fcst, M. Mari\u00f1o, J. Meier, I. Melnikov, P. Putrov, L. Schaposnik, E. Sharpe, S. Shatashvili, E. Silverstein, J. Song, J. Troost, and K. Ye for useful discussions and comments. This work is supported in part by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DESC0011632.\n\nPublished - 10.1007_2FJHEP11_2017_178.pdf
Submitted - 1707.01515.pdf
", "abstract": "We propose a way to define and compute invariants of general smooth 4-manifolds based on topological twists of non-Lagrangian 4d N=2 and N=3 theories in which the problem is reduced to a fairly standard computation in topological A-model, albeit with rather unusual targets, such as compact and non-compact Gepner models, asymmetric orbifolds, N=(2,2) linear dilaton theories, \"self-mirror\" geometries, varieties with complex multiplication, etc.", "date": "2017-11", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2017", "number": "11", "publisher": "Springer", "pagerange": "Art. No. 178", "id_number": "CaltechAUTHORS:20170720-171152878", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170720-171152878", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "SCOAP3" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" } ] }, "doi": "10.1007/JHEP11(2017)178", "primary_object": { "basename": "10.1007_2FJHEP11_2017_178.pdf", "url": "https://authors.library.caltech.edu/records/qr4fk-vrs74/files/10.1007_2FJHEP11_2017_178.pdf" }, "related_objects": [ { "basename": "1707.01515.pdf", "url": "https://authors.library.caltech.edu/records/qr4fk-vrs74/files/1707.01515.pdf" } ], "resource_type": "article", "pub_year": "2017", "author_list": "Gukov, Sergei" }, { "id": "https://authors.library.caltech.edu/records/7kxbt-v6s41", "eprint_id": 55045, "eprint_status": "archive", "datestamp": "2023-08-19 05:14:26", "lastmod": "2023-10-20 21:16:50", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Pei-Du", "name": { "family": "Pei", "given": "Du" }, "orcid": "0000-0001-5587-6905" } ] }, "title": "Equivariant Verlinde formula from fivebranes and vortices", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2017 Springer-Verlag GmbH Germany. \n\nReceived: 02 June 2016; Accepted: 03 May 2017; First Online: 03 July 2017. \n\nWe wish to thank Anton Alekseev for a wonderful set of notes [67] that we recommend to all the beginners. We also thank S. Shatashvili for discussions of this work in Fall 2013 and Spring 2014, which stimulated [60].We also benefited from discussions with Mina Aganagic, Sir Michael Atiyah, Tudor Dimofte, Abhijit Gadde, Jaume Gomis, Nigel Hitchin, Tadashi Okazaki, Satoshi Okuda, Pavel Putrov, Richard Wentworth and Wenbin Yan. This work is funded by the DOE Grant DE-SC0011632, NSF Grants DMS 1107452, 1107263, 1107367 (the GEAR Network), and the Walter Burke Institute for Theoretical Physics.\n\nSubmitted - 1501.01310v1.pdf
", "abstract": "We study complex Chern\u2013Simons theory on a Seifert manifold M_3 by embedding it into string theory. We show that complex Chern\u2013Simons theory on M_3 is equivalent to a topologically twisted supersymmetric theory and its partition function can be naturally regularized by turning on a mass parameter. We find that the dimensional reduction of this theory to 2d gives the low energy dynamics of vortices in four-dimensional gauge theory, the fact apparently overlooked in the vortex literature. We also generalize the relations between (1) the Verlinde algebra, (2) quantum cohomology of the Grassmannian, (3) Chern\u2013Simons theory on \u03a3\u00d7S^1 and (4) index of a spin^c Dirac operator on the moduli space of flat connections to a new set of relations between (1) the \"equivariant Verlinde algebra\" for a complex group, (2) the equivariant quantum K-theory of the vortex moduli space, (3) complex Chern\u2013Simons theory on \u03a3\u00d7S^1 and (4) the equivariant index of a spin^c Dirac operator on the moduli space of Higgs bundles.", "date": "2017-10", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "355", "number": "1", "publisher": "Springer", "pagerange": "1-50", "id_number": "CaltechAUTHORS:20150220-093858198", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150220-093858198", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "NSF", "grant_number": "DMS-1107452" }, { "agency": "NSF", "grant_number": "DMS-107263" }, { "agency": "NSF", "grant_number": "DMS-1107367" }, { "agency": "Walter Burke Institute for Theoretical Physics, Caltech" } ] }, "other_numbering_system": { "items": [ { "id": "2014-171", "name": "CALT-TH" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" } ] }, "doi": "10.1007/s00220-017-2931-9", "primary_object": { "basename": "1501.01310v1.pdf", "url": "https://authors.library.caltech.edu/records/7kxbt-v6s41/files/1501.01310v1.pdf" }, "resource_type": "article", "pub_year": "2017", "author_list": "Gukov, Sergei and Pei, Du" }, { "id": "https://authors.library.caltech.edu/records/kbxh0-6mm44", "eprint_id": 65404, "eprint_status": "archive", "datestamp": "2023-08-21 21:19:00", "lastmod": "2023-10-18 15:59:10", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Putrov-P", "name": { "family": "Putrov", "given": "Pavel" } }, { "id": "Vafa-C", "name": { "family": "Vafa", "given": "Cumrun" } } ] }, "title": "Fivebranes and 3-manifold homology", "ispublished": "pub", "full_text_status": "public", "keywords": "Chern-Simons Theories; Topological Field Theories; M-Theory Topological Strings", "note": "\u00a9 2017 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. \n\nReceived: 20 October 2016; Revised: 21 April 2017; Accepted: 05 June 2017; First Online: 14 July 2017. \n\nArticle funded by SCOAP3. \n\nWe would like to thank M. Aganagic, A. Gadde, M. Khovanov, C. Manolescu, S. Nawata, P. Ozsvath, J. Rasmussen, M. Romo, L. Rozansky, and E. Witten for useful comments and\ndiscussions. The work of S.G. is funded in part by the DOE Grant DE-SC0011632 and the Walter Burke Institute for Theoretical Physics. P.P. gratefully acknowledges support from the Institute for Advanced Study and also would like to thank Caltech and UT Austin theory groups for hospitality during the final stage of the project. The work of C.V. is supported in part by NSF grant PHY-1067976. C.V. would like to thank KITP for hospitality. Opinions and conclusions expressed here are those of the authors and do not necessarily reflect the views of funding agencies.\n\nPublished - 10.1007_2FJHEP07_2017_071.pdf
Submitted - 1602.05302v1.pdf
", "abstract": "Motivated by physical constructions of homological knot invariants, we study their analogs for closed 3-manifolds. We show that fivebrane compactifications provide a universal description of various old and new homological invariants of 3-manifolds. In terms of 3d/3d correspondence, such invariants are given by the Q-cohomology of the Hilbert space of partially topologically twisted 3d N=2 theory T[M_3] on a Riemann surface with defects. We demonstrate this by concrete and explicit calculations in the case of monopole/Heegaard Floer homology and a 3-manifold analog of Khovanov-Rozansky link homology. The latter gives a categorification of Chern-Simons partition function. Some of the new key elements include the explicit form of the S-transform and a novel connection between categorification and a previously mysterious role of Eichler integrals in Chern-Simons theory.", "date": "2017-07", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2017", "number": "07", "publisher": "Springer", "pagerange": "Art. No. 071", "id_number": "CaltechAUTHORS:20160316-162103450", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160316-162103450", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "Walter Burke Institute for Theoretical Physics, Caltech" }, { "agency": "Institute for Advanced Study" }, { "agency": "NSF", "grant_number": "PHY-1067976" }, { "agency": "SCOAP3" } ] }, "other_numbering_system": { "items": [ { "id": "2016-004", "name": "CALT-TH" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" } ] }, "doi": "10.1007/JHEP07(2017)071", "primary_object": { "basename": "10.1007_2FJHEP07_2017_071.pdf", "url": "https://authors.library.caltech.edu/records/kbxh0-6mm44/files/10.1007_2FJHEP07_2017_071.pdf" }, "related_objects": [ { "basename": "1602.05302v1.pdf", "url": "https://authors.library.caltech.edu/records/kbxh0-6mm44/files/1602.05302v1.pdf" } ], "resource_type": "article", "pub_year": "2017", "author_list": "Gukov, Sergei; Putrov, Pavel; et el." }, { "id": "https://authors.library.caltech.edu/records/ecwe3-ykz45", "eprint_id": 87406, "eprint_status": "archive", "datestamp": "2023-08-19 03:59:40", "lastmod": "2023-10-18 21:09:12", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Liu-Chiu-Chu-Melissa", "name": { "family": "Liu", "given": "Chiu-Chu Melissa" } }, { "id": "Sheshmani-A", "name": { "family": "Sheshmani", "given": "Artan" } }, { "id": "Yau-Shing-Tung", "name": { "family": "Yau", "given": "Shing-Tung" } } ] }, "title": "On topological approach to local theory of surfaces in Calabi\u2013Yau threefolds", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2018 International Press of Boston. \n\nSpecial Issue: Proceedings of the Strings 2016 Conference in Beijing\nGuest Editors: J. Maldacena (Institute for Advanced Study), H. Ooguri (California Institute of Technology), H. Babak (Harvard University), S. Li (Tsinghua University), W. Song (Tsinghua University), and H. Lin (Tsinghua University) \n\nWe would like to thank Jun Li, Davesh Maulik, and Richard Thomas for helpful conversations. The work of S. Gukov is supported in part by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632 and in part by the ERC Starting Grant no. 335739 \"Quantum fields and knot homologies\" funded by the European Research Council under the European Union Seventh Framework Programme. The work of C.-C. Liu is partially supported by NSF grants DMS-1206667 and DMS-1159416. A. Sheshmani would like to thank Kavli IPMU, MIT, Harvard and the Institute Henri Poincar\u00e9 (IHP) for creating the opportunity of initiating the discussions about the current article. The work of A. Sheshmani was partially supported by the World Premier International Research Center Initiative (WPI Initiative), MEXT, Japan and Laboratory of Mirror Symmetry NRU HSE, RF Government grant, ag. No 14.641.31.0001. S.-T. Y. was partially supported by NSF DMS-0804454, NSF PHY-1306313, and Simons 38558. The work of S.-T. Yau is partially supported by NSF grants DMS 1308244, DMS-159412, PHY-1306313, and PHY-0937443.\n\nAccepted Version - 1609.04363
", "abstract": "We study the web of dualities relating various enumerative invariants, notably Gromov\u2013Witten invariants and invariants that arise in topological gauge theory. In particular, we study Donaldson\u2013Thomas gauge theory and its reductions to D=4D=4 and D=2D=2 which are relevant to the local theory of surfaces in Calabi\u2013Yau threefolds.", "date": "2017-07", "date_type": "published", "publication": "Advances in Theoretical and Mathematical Physics", "volume": "21", "number": "7", "publisher": "International Press", "pagerange": "1679-1728", "id_number": "CaltechAUTHORS:20180627-133558358", "issn": "1095-0761", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180627-133558358", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "European Research Council (ERC)", "grant_number": "335739" }, { "agency": "NSF", "grant_number": "DMS-1206667" }, { "agency": "NSF", "grant_number": "DMS-1159416" }, { "agency": "Ministry of Education, Culture, Sports, Science and Technology (MEXT)", "grant_number": "14.641.31.0001" }, { "agency": "NSF", "grant_number": "DMS-0804454" }, { "agency": "NSF", "grant_number": "PHY-1306313" }, { "agency": "Simons Foundation", "grant_number": "38558" }, { "agency": "NSF", "grant_number": "DMS 1308244" }, { "agency": "NSF", "grant_number": "DMS-159412" }, { "agency": "NSF", "grant_number": "PHY-0937443" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" } ] }, "doi": "10.4310/ATMP.2017.v21.n7.a4", "primary_object": { "basename": "1609.04363", "url": "https://authors.library.caltech.edu/records/ecwe3-ykz45/files/1609.04363" }, "resource_type": "article", "pub_year": "2017", "author_list": "Gukov, Sergei; Liu, Chiu-Chu Melissa; et el." }, { "id": "https://authors.library.caltech.edu/records/fbvpk-8bc42", "eprint_id": 71990, "eprint_status": "archive", "datestamp": "2023-08-19 03:16:10", "lastmod": "2023-10-23 17:45:19", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" } ] }, "title": "RG Flows and Bifurcations", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2017 The Author. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3. \n\nReceived 21 December 2016, Revised 22 March 2017, Accepted 25 March 2017, Available online 29 March 2017. \n\nIt is a pleasure to thank O. Aharony, D. Gross, E. Kiritsis, I. Klebanov, N. Nekrasov, V. Rychkov, N. Seiberg, R. Shrock, D. Sullivan, R. Sundrum, G. Torroba, N. Warner, R. Wijewardhana and E. Witten for useful discussions and comments, and V. Lysov for collaboration during the early stages of this project and for his help with Fig. 6, Fig. 7, Fig. 8 ; Fig. 9. We also thank the anonymous referee for many insightful comments and gratefully acknowledge the warm hospitality of SCGP during the 2016 summer workshop, as well as participants and organizers of the GGI workshop (May 23\u2013July 8) and \"Strings 2016\" conference (August 1\u20135) where preliminary results of this work were presented. This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632. This work is also supported in part by the ERC Starting Grant no. 335739 \"Quantum fields and knot homologies\" funded by the European Research Council under the European Union Seventh Framework Programme.\n\nPublished - 1-s2.0-S0550321317301177-main.pdf
Submitted - 1608.06638v1.pdf
", "abstract": "Interpreting RG flows as dynamical systems in the space of couplings we produce a variety of constraints, global (topological) as well as local. These constraints, in turn, rule out some of the proposed RG flows and also predict new phases and fixed points, surprisingly, even in familiar theories such as O(N)O(N) model, QED_3, or QCD_4.", "date": "2017-06", "date_type": "published", "publication": "Nuclear Physics B", "volume": "919", "publisher": "Elsevier", "pagerange": "583-638", "id_number": "CaltechAUTHORS:20161114-105557935", "issn": "0550-3213", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161114-105557935", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "European Research Council (ERC)", "grant_number": "335739" }, { "agency": "SCOAP3" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" } ] }, "doi": "10.1016/j.nuclphysb.2017.03.025", "primary_object": { "basename": "1-s2.0-S0550321317301177-main.pdf", "url": "https://authors.library.caltech.edu/records/fbvpk-8bc42/files/1-s2.0-S0550321317301177-main.pdf" }, "related_objects": [ { "basename": "1608.06638v1.pdf", "url": "https://authors.library.caltech.edu/records/fbvpk-8bc42/files/1608.06638v1.pdf" } ], "resource_type": "article", "pub_year": "2017", "author_list": "Gukov, Sergei" }, { "id": "https://authors.library.caltech.edu/records/46gpz-ed792", "eprint_id": 66607, "eprint_status": "archive", "datestamp": "2023-08-20 11:05:33", "lastmod": "2023-10-18 18:37:33", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Chung-Hee-Joong", "name": { "family": "Chung", "given": "Hee-Joong" } }, { "id": "Dimofte-T-D", "name": { "family": "Dimofte", "given": "Tudor" } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Su\u0142kowski-Piotr", "name": { "family": "Su\u0142kowski", "given": "Piotr" }, "orcid": "0000-0002-6176-6240" } ] }, "title": "3d-3d Correspondence Revisited", "ispublished": "pub", "full_text_status": "public", "keywords": "Supersymmetric gauge theory, Topological Field Theories, Chern-Simons Theories, Supersymmetry and Duality", "note": "\u00a9 2016 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. \n\nArticle funded by SCOAP3. \n\nReceived: March 4, 2016; Accepted: April 13, 2016; Published: April 21, 2016. \n\nWe would like to thank S. Nawata, S. Razamat, B. Willett, and E. Witten for useful discussions.\nMany ideas in this paper were developed at the 2013 Simons Summer Workshop in\nMathematics and Physics, whose support and hospitality we gratefully acknowledge. The work of H.J.C. and S.G. is supported in part by DOE Grant DE-FG02-92ER40701. The\nwork of T.D. is supported in part by DOE grant DE-SC0009988. This work has also been\nsupported by the ERC Starting Grant no. 335739 \"Quantum fields and knot homologies\",\nfunded by the European Research Council under the European Union's Seventh Framework\nProgramme.\n\nPublished - art_3A10.1007_2FJHEP04_282016_29140.pdf
Submitted - 1405.3663.pdf
", "abstract": "In fivebrane compactifications on 3-manifolds, we point out the importance of all flat connections in the proper definition of the effective 3d N=2 \ntheory. The Lagrangians of some theories with the desired properties can be constructed with the help of homological knot invariants that categorify colored Jones polynomials. Higgsing the full 3d theories constructed this way recovers theories found previously by Dimofte-Gaiotto-Gukov. We also consider the cutting and gluing of 3-manifolds along smooth boundaries and the role played by all flat connections in this operation.", "date": "2016-04", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2016", "number": "4", "publisher": "Springer", "pagerange": "Art. No. 140", "id_number": "CaltechAUTHORS:20160503-083907514", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160503-083907514", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG02-92ER40701" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0009988" }, { "agency": "European Research Council (ERC)", "grant_number": "335739" }, { "agency": "SCOAP3" } ] }, "doi": "10.1007/JHEP04(2016)140", "primary_object": { "basename": "1405.3663.pdf", "url": "https://authors.library.caltech.edu/records/46gpz-ed792/files/1405.3663.pdf" }, "related_objects": [ { "basename": "art_3A10.1007_2FJHEP04_282016_29140.pdf", "url": "https://authors.library.caltech.edu/records/46gpz-ed792/files/art_3A10.1007_2FJHEP04_282016_29140.pdf" } ], "resource_type": "article", "pub_year": "2016", "author_list": "Chung, Hee-Joong; Dimofte, Tudor; et el." }, { "id": "https://authors.library.caltech.edu/records/a4ag2-0qb96", "eprint_id": 63644, "eprint_status": "archive", "datestamp": "2023-08-20 10:48:09", "lastmod": "2023-10-17 15:24:19", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Nawata-Satoshi", "name": { "family": "Nawata", "given": "Satoshi" } }, { "id": "Saberi-Ingmar-A", "name": { "family": "Saberi", "given": "Ingmar" } }, { "id": "Sto\u0161i\u0107-M", "name": { "family": "Sto\u0161i\u0107", "given": "Marko" } }, { "id": "Su\u0142kowski-Piotr", "name": { "family": "Su\u0142kowski", "given": "Piotr" }, "orcid": "0000-0002-6176-6240" } ] }, "title": "Sequencing BPS Spectra", "ispublished": "pub", "full_text_status": "public", "keywords": "Differential and Algebraic Geometry, Supersymmetry and Duality, Topological\nField Theories, Topological Strings", "note": "\u00a9 2016 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. \n\n\nArticle funded by SCOAP3. \n\nReceived: January 9, 2016; Accepted: February 15, 2016; Published: March 2, 2016. \n\nS.N. would like to express deep gratitude to the previous institutions, NIKHEF Amsterdam, University of Warsaw and Max Planck Institute for Mathematics at Bonn where most of this work was carried out.\nThis work has been supported by the ERC Starting Grant no. 335739 \"Quantum fields and knot homologies\", funded by the European Research Council under the European Union's Seventh Framework Programme, and by Walter Burke Institute for Theoretical Physics, California Institute of Technology. The work of S.G. is partially supported by the DOE Grant DE-SC0011632. The work of S.N. is partially supported by the ERC Advanced Grant no. 246974, \"Supersymmetry: a window to non-perturbative physics\", and also partially supported by the center of excellence grant \"Center for Quantum Geometry of Moduli Spaces (QGM)\" from the Danish National Research Foundation. M.S. was also partially supported by the Ministry of Education of Serbia, grant no. 174012. P.S. acknowledges the support of the Foundation for Polish Science.\n\nPublished - art_10.1007_JHEP03_2016_004.pdf
Submitted - 1512.07883v2.pdf
", "abstract": "This paper provides both a detailed study of color-dependence of link homologies, as realized in physics as certain spaces of BPS states, and a broad study of the behavior of BPS states in general. We consider how the spectrum of BPS states varies as continuous parameters of a theory are perturbed. This question can be posed in a wide variety of physical contexts, and we answer it by proposing that the relationship between unperturbed and perturbed BPS spectra is described by a spectral sequence. These general considerations unify previous applications of spectral sequence techniques to physics, and explain from a physical standpoint the appearance of many spectral sequences relating various link homology theories to one another. We also study structural properties of colored HOMFLY homology for links and evaluate Poincar\u00e9 polynomials in numerous examples. Among these structural properties is a novel \"sliding\" property, which can be explained by using (refined) modular S-matrix. This leads to the identification of modular transformations in Chern-Simons theory and 3d N=2 theory via the 3d/3d correspondence. Lastly, we introduce the notion of associated varieties as classical limits of recursion relations of colored superpolynomials of links, and study their properties.", "date": "2016-03-02", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2016", "number": "03", "publisher": "Springer", "pagerange": "Art. No. 004", "id_number": "CaltechAUTHORS:20160113-131017250", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160113-131017250", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "European Research Council (ERC)", "grant_number": "335739" }, { "agency": "Walter Burke Institute for Theoretical Physics, Caltech" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "European Research Council (ERC)", "grant_number": "246974" }, { "agency": "Danish Research Council" }, { "agency": "Ministry of Education (Serbia)", "grant_number": "174012" }, { "agency": "Foundation for Polish Science" }, { "agency": "SCOAP3" } ] }, "other_numbering_system": { "items": [ { "id": "2015-063", "name": "CALT-TH" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" } ] }, "doi": "10.1007/JHEP03(2016)004", "primary_object": { "basename": "1512.07883v2.pdf", "url": "https://authors.library.caltech.edu/records/a4ag2-0qb96/files/1512.07883v2.pdf" }, "related_objects": [ { "basename": "art_10.1007_JHEP03_2016_004.pdf", "url": "https://authors.library.caltech.edu/records/a4ag2-0qb96/files/art_10.1007_JHEP03_2016_004.pdf" } ], "resource_type": "article", "pub_year": "2016", "author_list": "Gukov, Sergei; Nawata, Satoshi; et el." }, { "id": "https://authors.library.caltech.edu/records/qjp7q-zgn07", "eprint_id": 66440, "eprint_status": "archive", "datestamp": "2023-08-22 17:29:25", "lastmod": "2023-10-18 18:05:18", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Elliot-R", "name": { "family": "Elliot", "given": "Ross" } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" } ] }, "title": "Exceptional knot homology", "ispublished": "pub", "full_text_status": "public", "keywords": "BPS states; double affine Hecke algebras; superpolynomials; knot homology; quantum invariants; exceptional Lie algebras; singularity theory; Landau\u2013Ginzburg potential", "note": "\u00a9 2016 World Scientific Publishing Co Pte Ltd. \n\nReceived: 31 July 2015; Accepted: 21 December 2015; Published: 1 February 2016. \n\nOur special thanks go to Ivan Cherednik, who provided the formulas for DAHA-Jones polynomials and participated in the development of many ideas contained herein. Without his contributions, this work would not be possible. \n\nWe would also like to thank J. Adams, M. Aschbacher, D. Bar-Natan, P. Cvitanovi\u0107 , W.A. de Graaf, A. Gabrielov, and S. Morrison for helpful discussions. The work of S.G. is funded in part by the DOE Grant DE-SC0011632 and the Walter Burke Institute for Theoretical Physics. The work of R.E. is partially supported by a Troesh Family Graduate Fellowship 2014-15.\n\nSubmitted - 1505.01635v1.pdf
", "abstract": "The goal of this paper is twofold. First, we find a natural home for the double affine Hecke algebras (DAHA) in the physics of BPS states. Second, we introduce new invariants of torus knots and links called hyperpolynomials that address the \"problem of negative coefficients\" often encountered in DAHA-based approaches to homological invariants of torus knots and links. Furthermore, from the physics of BPS states and the spectra of singularities associated with Landau\u2013Ginzburg potentials, we also describe a rich structure of differentials that act on homological knot invariants for exceptional groups and uniquely determine the latter for torus knots.", "date": "2016-03", "date_type": "published", "publication": "Journal of Knot Theory and its Ramifications", "volume": "25", "number": "3", "publisher": "World Scientific Publishing Co.", "pagerange": "Art. No. 1640003", "id_number": "CaltechAUTHORS:20160425-090534476", "issn": "0218-2165", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160425-090534476", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "Troesh Family Graduate Fellowship 2014-15" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" } ] }, "doi": "10.1142/S0218216516400034", "primary_object": { "basename": "1505.01635v1.pdf", "url": "https://authors.library.caltech.edu/records/qjp7q-zgn07/files/1505.01635v1.pdf" }, "resource_type": "article", "pub_year": "2016", "author_list": "Elliot, Ross and Gukov, Sergei" }, { "id": "https://authors.library.caltech.edu/records/822wv-zxz21", "eprint_id": 55717, "eprint_status": "archive", "datestamp": "2023-08-20 09:39:55", "lastmod": "2023-10-20 23:03:47", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" } ] }, "title": "Counting RG flows", "ispublished": "pub", "full_text_status": "public", "keywords": "Supersymmetric gauge theory, Renormalization Group", "note": "\u00a9 2016 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. \n\nArticle funded by SCOAP3. \n\nReceived: September 2, 2015; Accepted: December 20, 2015; Published: January 5, 2016. \n\nI would like to thank N. Deger, L. Dixon, K. Intriligator, V. Lysov, Yu Nakayama, H. Ooguri, L. Rastelli, D. Roggenkamp, E. Sezgin, A. Shapere, M. Strassler, R. Sundrum, D. Xie, and W. Yan for useful discussions and comments. It is also a pleasure to thank the organizers and participants of the conference \"Progress and Application of Modern QFT\" in Aspen Feb. 16-21, 2015, where I had the opportunity to discuss the results presented here. This work is funded by the DOE Grant DE-SC0011632 and the Walter Burke Institute for Theoretical Physics.\n\nPublished - art_10.1007_JHEP01_2016_020.pdf
Submitted - 1503.01474v1__1_.pdf
", "abstract": "Interpreting renormalization group flows as solitons interpolating between different fixed points, we ask various questions that are normally asked in soliton physics but not in renormalization theory. Can one count RG flows? Are there different \"topological sectors\" for RG flows? What is the moduli space of an RG flow, and how does it compare to familiar moduli spaces of (supersymmetric) dowain walls? Analyzing these questions in a wide variety of contexts \u2014 from counting RG walls to AdS/CFT correspondence \u2014 will not only provide favorable answers, but will also lead us to a unified general framework that is powerful enough to account for peculiar RG flows and predict new physical phenomena. Namely, using Bott's version of Morse theory we relate the topology of conformal manifolds to certain properties of RG flows that can be used as precise diagnostics and \"topological obstructions\" for the strong form of the C-theorem in any dimension. Moreover, this framework suggests a precise mechanism for how the violation of the strong C-theorem happens and predicts \"phase transitions\" along the RG flow when the topological obstruction is non-trivial. Along the way, we also find new conformal manifolds in well-known 4d CFT's and point out connections with the superconformal index and classifying spaces of global symmetry groups.", "date": "2016-01", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2016", "number": "1", "publisher": "Springer", "pagerange": "Art. No. 020", "id_number": "CaltechAUTHORS:20150311-193040484", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150311-193040484", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "Walter Burke Institute for Theoretical Physics, Caltech" }, { "agency": "SCOAP3" } ] }, "other_numbering_system": { "items": [ { "id": "2015-10", "name": "CALT-TH" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" } ] }, "doi": "10.1007/JHEP01(2016)020", "primary_object": { "basename": "1503.01474v1__1_.pdf", "url": "https://authors.library.caltech.edu/records/822wv-zxz21/files/1503.01474v1__1_.pdf" }, "related_objects": [ { "basename": "art_10.1007_JHEP01_2016_020.pdf", "url": "https://authors.library.caltech.edu/records/822wv-zxz21/files/art_10.1007_JHEP01_2016_020.pdf" } ], "resource_type": "article", "pub_year": "2016", "author_list": "Gukov, Sergei" }, { "id": "https://authors.library.caltech.edu/records/f5eey-eyb55", "eprint_id": 64761, "eprint_status": "archive", "datestamp": "2023-08-20 09:44:09", "lastmod": "2023-10-17 21:51:36", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frenkel-E", "name": { "family": "Frenkel", "given": "Edward" } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Teschner-J", "name": { "family": "Teschner", "given": "J\u00f6rg" } } ] }, "title": "Surface operators and separation of variables", "ispublished": "pub", "full_text_status": "public", "keywords": "Brane Dynamics in Gauge Theories, Supersymmetric gauge theory", "note": "\u00a9 2016 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. \n\nReceived: September 19, 2015; Accepted: December 10, 2015; Published: January 29, 2016. \n\nArticle funded by SCOAP3. \n\nWe would like to thank D. Gaiotto, K. Maruyoshi, and N. Nekrasov for useful discussions and comments. The research of E.F. was supported by the NSF grants DMS-1160328 and DMS-1201335. The work of S.G. is funded in part by the DOE Grant DE-SC0011632 and the Walter Burke Institute for Theoretical Physics.\n\nPublished - art_10.1007_JHEP01_2016_179.pdf
Submitted - 1506.07508v1.pdf
", "abstract": "Alday, Gaiotto, and Tachikawa conjectured relations between certain 4d N = 2 supersymmetric field theories and 2d Liouville conformal field theory. We study generalizations of these relations to 4d theories with surface operators. For one type of surface operators the corresponding 2d theory is the WZW model, and for another type \u2014 the Liouville theory with insertions of extra degenerate fields. We show that these two 4d theories with surface operators exhibit an IR duality, which reflects the known relation (the so-called separation of variables) between the conformal blocks of the WZW model and the Liouville theory. Furthermore, we trace this IR duality to a brane creation construction relating systems of M5 and M2 branes in M-theory. Finally, we show that this duality may be expressed as an explicit relation between the generating functions for the changes of variables between natural sets of Darboux coordinates on the Hitchin moduli space.", "date": "2016-01", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2016", "number": "1", "publisher": "Springer", "pagerange": "Art. No. 179", "id_number": "CaltechAUTHORS:20160225-125012315", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160225-125012315", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "SCOAP3" }, { "agency": "NSF", "grant_number": "DMS-1160328" }, { "agency": "NSF", "grant_number": "DMS-1201335" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "Walter Burke Institute for Theoretical Physics, Caltech" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" } ] }, "doi": "10.1007/JHEP01(2016)179", "primary_object": { "basename": "1506.07508v1.pdf", "url": "https://authors.library.caltech.edu/records/f5eey-eyb55/files/1506.07508v1.pdf" }, "related_objects": [ { "basename": "art_10.1007_JHEP01_2016_179.pdf", "url": "https://authors.library.caltech.edu/records/f5eey-eyb55/files/art_10.1007_JHEP01_2016_179.pdf" } ], "resource_type": "article", "pub_year": "2016", "author_list": "Frenkel, Edward; Gukov, Sergei; et el." }, { "id": "https://authors.library.caltech.edu/records/jkcz6-yba75", "eprint_id": 47267, "eprint_status": "archive", "datestamp": "2023-08-20 00:48:20", "lastmod": "2023-10-26 20:27:18", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gadde-A", "name": { "family": "Gadde", "given": "Abhijit" } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Putrov-P", "name": { "family": "Putrov", "given": "Pavel" } } ] }, "title": "Walls, lines, and spectral dualities in 3d gauge theories", "ispublished": "pub", "full_text_status": "public", "note": "Open Access \u00a9 The Authors. Article funded by SCOAP3.\n\nReceived: February 15, 2014\nAccepted: April 12, 2014\nPublished: May 12, 2014.\n\nWe thank C. Beem, A. Bytsko, T. Dimofte, A. Gorsky, S. Nawata, N. Nekrasov,\nS. Shatashvili, P. Su lkowski, R. van der Veen for useful discussions on related topics. The\nwork of A.G. is supported in part by the John A. McCone fellowship and by DOE Grant DE-FG02-92-ER40701. The work of S.G. is supported in part by DOE Grant DE-FG03-92-ER40701FG-02 and in part by NSF Grant PHY-0757647. The work of P.P. is supported in part by the Sherman Fairchild scholarship and by NSF Grant PHY-1050729. Opinions and conclusions expressed here are those of the authors and do not necessarily reflect the\nviews of funding agencies.\n\nPublished - scoap3-fulltext.pdf
", "abstract": "In this paper we analyze various half-BPS defects in a general three dimensional N = 2 supersymmetric gauge theory T. They correspond to closed paths in SUSY parameter space and their tension is computed by evaluating period integrals along these paths. In addition to such defects, we also study wall defects that interpolate between\nT and its SL(2,Z) transform by coupling the 3d theory to a 4d theory with S-duality wall. We propose a novel spectral duality between 3d gauge theories and integrable systems. This duality complements a similar duality discovered by Nekrasov and Shatashvili. As\nanother application, for 3d N = 2 theories associated with knots and 3-manifolds we compute periods of (super)A-polynomial curves and relate the results with the spectrum of\ndomain walls and line operators.", "date": "2014-05", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2014", "number": "5", "publisher": "Springer", "pagerange": "Art. No. 47", "id_number": "CaltechAUTHORS:20140716-113255164", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20140716-113255164", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701FG-02" }, { "agency": "NSF", "grant_number": "PHY-0757647" }, { "agency": "Sherman Fairchild Foundation" }, { "agency": "NSF", "grant_number": "PHY-1050729" }, { "agency": "John A. McCone Fellowship" } ] }, "other_numbering_system": { "items": [ { "id": "68-2905", "name": "CALT" } ] }, "local_group": { "items": [ { "id": "Caltech-Theory" } ] }, "doi": "10.1007/JHEP05(2014)047", "primary_object": { "basename": "scoap3-fulltext.pdf", "url": "https://authors.library.caltech.edu/records/jkcz6-yba75/files/scoap3-fulltext.pdf" }, "resource_type": "article", "pub_year": "2014", "author_list": "Gadde, Abhijit; Gukov, Sergei; et el." }, { "id": "https://authors.library.caltech.edu/records/5nkxm-abj06", "eprint_id": 45783, "eprint_status": "archive", "datestamp": "2023-08-20 00:01:33", "lastmod": "2023-10-26 18:27:27", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gadde-A", "name": { "family": "Gadde", "given": "Abhijit" } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Putrov-P", "name": { "family": "Putrov", "given": "Pavel" } } ] }, "title": "(0, 2) trialities", "ispublished": "pub", "full_text_status": "public", "keywords": "Supersymmetric gauge theory, Supersymmetry and Duality, Supersymmetry\nBreaking", "note": "\u00a9 2014 The Authors.\n\nThis article is distributed under the terms of the Creative Commons\nAttribution License (CC-BY 4.0), which permits any use, distribution and reproduction in\nany medium, provided the original author(s) and source are credited.\n\nArticle funded by SCOAP3.\nPublished for SISSA by Springer.\n\nReceived: December 25, 2013;\nAccepted: February 23, 2014;\nPublished: March 17, 2014.\n\nWe would like to thank F. Benini, N. Bobev, N. Seiberg, E. Sharpe, M. Shifman, A. Vain\nshtein and E. Witten for useful discussions. The work of A.G. is supported in part by\nthe John A. McCone fellowship and by DOE Grant DE-FG02-92-ER40701. The work of\nS.G. is supported in part by DOE Grant DE-FG03-92-ER40701FG-02. The work of P.P. is\nsupported in part by the Sherman Fairchild scholarship and by NSF Grant PHY-1050729.\nWe would like to thank the Aspen Center for Physics and the 2013 Simons Workshop in\nMathematics and Physics for hospitality during various states of this work. The Aspen\nCenter for Physics is supported in part by the National Science Foundation under Grant\nNo. PHYS-1066293. Opinions and conclusions expressed here are those of the authors and\ndo not necessarily reflect the views of funding agencies.\n\nPublished - art_10.1007_JHEP03_2014_076.pdf
Submitted - 1310.0818v2.pdf
", "abstract": "Motivated by the connection between 4-manifolds and 2d N = (0, 2) theories,\nwe study the dynamics of a fairly large class of 2d N = (0, 2) gauge theories. We see that\nphysics of such theories is very rich, much as the physics of 4d N = 1 theories. We discover\na new type of duality that is very reminiscent of the 4d Seiberg duality. Surprisingly, the\nnew 2d duality is an operation of order three: it is IR equivalence of three different theories\nand, as such, is actually a triality. We also consider quiver theories and study their triality\nwebs. Given a quiver graph, we find that supersymmetry is dynamically broken unless the\nranks of the gauge groups and flavor groups satisfy stringent inequalities. In fact, for most\nof the graphs these inequalities have no solutions. This supports the folklore theorem that\ngeneric 2d N = (0, 2) theories break supersymmetry dynamically.", "date": "2014-03-17", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2014", "number": "3", "publisher": "Springer", "pagerange": "Art. No. 76", "id_number": "CaltechAUTHORS:20140516-074913803", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20140516-074913803", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "John A. McCone Fellowship" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG02-92-ER40701" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701FG-02" }, { "agency": "Sherman Fairchild Foundation" }, { "agency": "NSF", "grant_number": "PHY-1050729" }, { "agency": "NSF", "grant_number": "PHYS-1066293" } ] }, "local_group": { "items": [ { "id": "Caltech-Theory" } ] }, "doi": "10.1007/JHEP03(2014)076", "primary_object": { "basename": "1310.0818v2.pdf", "url": "https://authors.library.caltech.edu/records/5nkxm-abj06/files/1310.0818v2.pdf" }, "related_objects": [ { "basename": "art_10.1007_JHEP03_2014_076.pdf", "url": "https://authors.library.caltech.edu/records/5nkxm-abj06/files/art_10.1007_JHEP03_2014_076.pdf" } ], "resource_type": "article", "pub_year": "2014", "author_list": "Gadde, Abhijit; Gukov, Sergei; et el." }, { "id": "https://authors.library.caltech.edu/records/78zmy-jdm57", "eprint_id": 45181, "eprint_status": "archive", "datestamp": "2023-08-20 00:01:26", "lastmod": "2023-10-26 17:37:12", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gadde-A", "name": { "family": "Gadde", "given": "Abhijit" } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" } ] }, "title": "2d index and surface operators", "ispublished": "pub", "full_text_status": "public", "keywords": "Supersymmetric gauge theory, Brane Dynamics in Gauge Theories", "note": "\u00a9 2014 The Authors. \n\nThis article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in\nany medium, provided the original author(s) and source are credited. Article funded by SCOAP^3.\n\nReceived: December 25, 2013. Accepted: February 20, 2014. Published: March 17, 2014. Available under Open Access. \n\nThe authors would like to thank Yu Nakayama, Hirosi Ooguri, Pavel Putrov and Shlomo Razamat for interesting discussions. Authors are especially grateful to Anton Kapustin for his valuable comments. The work of A.G. is supported in part by the John A. McCone fellowship and by DOE Grant DE-FG02-92-ER40701. The work of S.G. is supported in part by DOE Grant DE-FG03-92-ER40701FG-02 and in part by NSF Grant PHY-0757647. Opinions and conclusions expressed here are those of the authors and do not necessarily reflect the views of funding agencies.\n\nPublished - art_10.1007_JHEP03_2014_080.pdf
Submitted - 1305.0266v2.pdf
", "abstract": "In this paper we compute the superconformal index of 2d (2, 2) supersymmetric gauge theories. The 2d superconformal index, a.k.a. flavored elliptic genus, is computed by a unitary matrix integral much like the matrix integral that computes the 4d superconformal index. We compute the 2d index explicitly for a number of examples. In the case of abelian gauge theories we see that the index is invariant under flop transition and under CY-LG correspondence. The index also provides a powerful check of the Seiberg-type duality for non-abelian gauge theories discovered by Hori and Tong.\n\nIn the later half of the paper, we study half-BPS surface operators in N = 2 super-conformal gauge theories. They are engineered by coupling the 2d (2, 2) supersymmetric gauge theory living on the support of the surface operator to the 4d N = 2 theory, so that different realizations of the same surface operator with a given Levi type are related by a 2d analogue of the Seiberg duality. The index of this coupled system is computed by using the tools developed in the first half of the paper. The superconformal index in the presence of surface defect is expected to be invariant under generalized S-duality. We demonstrate that it is indeed the case. In doing so the Seiberg-type duality of the 2d theory plays an important role.", "date": "2014-03-17", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2014", "number": "3", "publisher": "Springer", "pagerange": "Art. No. 80", "id_number": "CaltechAUTHORS:20140424-092625660", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20140424-092625660", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "John A. McCone Fellowship" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG02-92-ER40701" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701FG-02" }, { "agency": "NSF", "grant_number": "PHY-0757647" } ] }, "local_group": { "items": [ { "id": "Caltech-Theory" } ] }, "doi": "10.1007/JHEP03(2014)080", "primary_object": { "basename": "1305.0266v2.pdf", "url": "https://authors.library.caltech.edu/records/78zmy-jdm57/files/1305.0266v2.pdf" }, "related_objects": [ { "basename": "art_10.1007_JHEP03_2014_080.pdf", "url": "https://authors.library.caltech.edu/records/78zmy-jdm57/files/art_10.1007_JHEP03_2014_080.pdf" } ], "resource_type": "article", "pub_year": "2014", "author_list": "Gadde, Abhijit and Gukov, Sergei" }, { "id": "https://authors.library.caltech.edu/records/748zw-qnd04", "eprint_id": 43760, "eprint_status": "archive", "datestamp": "2023-08-19 22:53:00", "lastmod": "2023-10-25 23:50:56", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Dimofte-T-D", "name": { "family": "Dimofte", "given": "Tudor" } }, { "id": "Gaiotto-D", "name": { "family": "Gaiotto", "given": "Davide" } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" } ] }, "title": "Gauge Theories Labelled by Three-Manifolds", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2013 Springer-Verlag Berlin Heidelberg. \n\nReceived: 15 May 2012. Accepted: 6 July 2013. Published online: 15 December 2013. \n\nWe wish to thank A. Kapustin, N. Seiberg, C. Vafa, R. van der Veen, and E. Witten for many helpful and enlightening discussions. The work of TD is supported in part by NSF Grant PHY-0969448. The work of DG is supported in part by NSF grant PHY-0503584 and in part by the Roger Dashen membership in the Institute for Advanced Study. The work of SG is supported in part by DOE Grant DE-FG03-92-ER40701 and in part by NSF Grant PHY-0757647. TD and SG thank the Kavli Institute for Theoretical Physics (research\nsupported by DARPA under Grant No. HR0011-09-1-0015 and by the National Science Foundation under Grant No. PHY05-51164 and the Simons Center for Geometry and Physics for their hospitality in the summer of 2011. TD also acknowledges the Max Planck Institut f\u00fcr Mathematik for its hospitality and support during June, 2011. Opinions and conclusions expressed here are those of the authors and do not necessarily reflect the views of funding agencies. Communicated by N. A. Nekrasov\n\nSubmitted - 1108.4389v1.pdf
", "abstract": "We propose a dictionary between geometry of triangulated 3-manifolds and physics of three-dimensional N=2 gauge theories. Under this duality, standard operations on triangulated 3-manifolds and various invariants thereof (classical as well as quantum) find a natural interpretation in field theory. For example, independence of the SL(2) Chern-Simons partition function on the choice of triangulation translates to a statement that S^3_b partition functions of two mirror 3d N=2 gauge theories are equal. Three-dimensional N=2 field theories associated to 3-manifolds can be thought of as theories that describe boundary conditions and duality walls in four-dimensional N=2 SCFTs, thus making the whole construction functorial with respect to cobordisms and gluing.", "date": "2014-01", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "325", "number": "2", "publisher": "Springer", "pagerange": "367-419", "id_number": "CaltechAUTHORS:20140210-154717900", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20140210-154717900", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-0969448" }, { "agency": "NSF", "grant_number": "PHY-0503584" }, { "agency": "Institute for Advanced Study" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" }, { "agency": "NSF", "grant_number": "PHY-0757647" }, { "agency": "Defense Advanced Research Projects Agency (DARPA)", "grant_number": "HR0011-09-1-0015" }, { "agency": "NSF", "grant_number": "PHY05-51164" }, { "agency": "Simons Center for Geometry and Physics" }, { "agency": "Max Planck Institut f\u00fcr Mathematik" } ] }, "other_numbering_system": { "items": [ { "id": "68-2847", "name": "CALT" } ] }, "local_group": { "items": [ { "id": "Caltech-Theory" } ] }, "doi": "10.1007/s00220-013-1863-2", "primary_object": { "basename": "1108.4389v1.pdf", "url": "https://authors.library.caltech.edu/records/748zw-qnd04/files/1108.4389v1.pdf" }, "resource_type": "article", "pub_year": "2014", "author_list": "Dimofte, Tudor; Gaiotto, Davide; et el." }, { "id": "https://authors.library.caltech.edu/records/9xkv9-1s605", "eprint_id": 42237, "eprint_status": "archive", "datestamp": "2023-08-19 21:27:11", "lastmod": "2023-10-25 15:46:22", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gaiotto-D", "name": { "family": "Gaiotto", "given": "Davide" } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Seiberg-N", "name": { "family": "Seiberg", "given": "Nathan" }, "orcid": "0000-0003-3897-046X" } ] }, "title": "Surface defects and resolvents", "ispublished": "pub", "full_text_status": "public", "keywords": "Supersymmetric gauge theory, Nonperturbative Effects, Sigma Models", "note": "\u00a9 SISSA 2013. Published for SISSA by Springer. \n\nReceived: July 27, 2013. Accepted: August 21, 2013. Published: September 12, 2013. \n\nWe are grateful to A. Kapustin for collaboration at an early stage of the project, and many important discussions. The research of DG was supported by the Perimeter Institute for Theoretical Physics. Research at Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Economic Development and Innovation. The work of SG is supported in part by DOE Grant DE-FG03-92-ER40701FG-02. The work of NS was supported in part by DOE grant DE-SC0009988 and by the United States-Israel Binational Science Foundation (BSF) under grant number 2010/629. Opinions and conclusions expressed here are those of the authors and do not necessarily reflect the views of funding agencies.\n\nSubmitted - 1307.2578v2.pdf
", "abstract": "We study a large class of BPS surface defects in 4d N=2 gauge theories. They are defined by coupling a 2d N=(2,2) gauged linear sigma model to the 4d bulk degrees of freedom. Our main result is an efficient computation of the effective twisted superpotential for all these models in terms of a basic object closely related to the resolvent of the 4d gauge theory, which encodes the curve describing the 4d low energy dynamics. We reproduce and extend the results of brane constructions and compute the effective twisted superpotential for general monodromy surface defects. We encounter novel, puzzling field theory phenomena in the low energy dynamics of the simplest surface defects and we propose some local models to explain them. We also study in some detail the behavior of surface defects near monopole points of the bulk theory's Coulomb branch. Finally, we explore the effect on the defect of breaking the bulk supersymmetry from N=2 to N=1 and show that certain quantities are independent of this breaking.", "date": "2013-09-12", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2013", "number": "9", "publisher": "Springer", "pagerange": "Art. No. 70", "id_number": "CaltechAUTHORS:20131105-071959496", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20131105-071959496", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Perimeter Institute for Theoretical Physics" }, { "agency": "Industry Canada" }, { "agency": "Ontario Ministry of Economic Development and Innovation" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701FG-02" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0009988" }, { "agency": "Binational Science Foundation (United States-Israel)", "grant_number": "2010/629" } ] }, "doi": "10.1007/JHEP09(2013)070", "primary_object": { "basename": "1307.2578v2.pdf", "url": "https://authors.library.caltech.edu/records/9xkv9-1s605/files/1307.2578v2.pdf" }, "resource_type": "article", "pub_year": "2013", "author_list": "Gaiotto, Davide; Gukov, Sergei; et el." }, { "id": "https://authors.library.caltech.edu/records/g3624-qce87", "eprint_id": 41323, "eprint_status": "archive", "datestamp": "2023-08-19 19:45:35", "lastmod": "2023-10-24 23:38:46", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Dimofte-T-D", "name": { "family": "Dimofte", "given": "Tudor" } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" } ] }, "title": "Chern-Simons theory and S-duality", "ispublished": "pub", "full_text_status": "public", "keywords": "Duality in Gauge Field Theories, Chern-Simons Theories, Topological Field\nTheories, Supersymmetric gauge theory", "note": "\u00a9 2013 SISSA. Published for SISSA by Springer.\n\nReceived: March 16, 2013. Accepted: April 20, 2013. Published: May 21, 2013. \n\nWe wish thank G. Mikhalkin, G. Moore, A. Neitzke, R. van der Veen, D. Zagier, and especially D. Gaiotto and J. Teschner for many enlightening and helpful discussions. We would also like to thank the Aspen Center for Physics for their hospitality during the 2010 Summer Program, where some of the ideas presented here originated. The work of TD is supported in part by NSF Grant PHY-0969448. The work of SG is supported in part by DOE Grant DE-FG03-92-ER40701 and in part by NSF Grant PHY-0757647. Opinions and conclusions expressed here are those of the authors and do not necessarily reflect the\nviews of funding agencies.\n\nSubmitted - 1106.4550v1.pdf
", "abstract": "We study S-dualities in analytically continued SL(2) Chern-Simons theory on a 3-manifold M. By realizing Chern-Simons theory via a compactification of a 6d five-brane theory on M, various objects and symmetries in Chern-Simons theory become related to objects and operations in dual 2d, 3d, and 4d theories. For example, the space of flat SL(2, C ) connections on M is identified with the space of supersymmetric vacua in a dual 3d gauge theory. The hidden symmetry h \u2192 -4\u03c0^2/h of SL(2) Chern-Simons theory can be identified as the S-duality transformation of N=4 super-Yang-Mills theory (obtained by compactifying the five-brane theory on a torus); whereas the mapping class group action in Chern-Simons theory on a three-manifold M with boundary C is realized as S-duality in 4d N=2 super-Yang-Mills theory associated with the Riemann surface C. We illustrate these symmetries by considering simple examples of 3-manifolds that include knot complements and punctured torus bundles, on the one hand, and mapping cylinders associated with mapping class group transformations, on the other. A generalization of mapping class group actions further allows us to study the transformations between several distinguished coordinate systems on the phase space of Chern-Simons theory, the SL(2) Hitchin moduli space.", "date": "2013-05", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2013", "number": "5", "publisher": "Springer", "pagerange": "Art. No. 109", "id_number": "CaltechAUTHORS:20130913-112827417", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130913-112827417", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-0969448" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" }, { "agency": "NSF", "grant_number": "PHY-0757647" } ] }, "local_group": { "items": [ { "id": "Caltech-Theory" } ] }, "doi": "10.1007/JHEP05(2013)109", "primary_object": { "basename": "1106.4550v1.pdf", "url": "https://authors.library.caltech.edu/records/g3624-qce87/files/1106.4550v1.pdf" }, "resource_type": "article", "pub_year": "2013", "author_list": "Dimofte, Tudor and Gukov, Sergei" }, { "id": "https://authors.library.caltech.edu/records/70w97-98w52", "eprint_id": 36133, "eprint_status": "archive", "datestamp": "2023-08-19 14:39:28", "lastmod": "2023-10-20 22:16:33", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Fuji-Hiroyuki", "name": { "family": "Fuji", "given": "Hiroyuki" } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Su\u0142kowski-Piotr", "name": { "family": "Su\u0142kowski", "given": "Piotr" }, "orcid": "0000-0002-6176-6240" } ] }, "title": "Super-A-polynomial for knots and BPS states", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2012 Elsevier B.V. \n\nReceived 6 June 2012; accepted 9 October 2012. Available online 13 October 2012. \n\nWe thank M. Aganagic, R. Dijkgraaf, E. Gorsky, A. Mironov, A. Morozov, L. Ng, M. Sto\u0161i\u0107, and C. Vafa for useful discussions on related topics. The work of H.F. is supported by the Grant-in-Aid for Young Scientists (B) [# 21740179] from the Japan Ministry of Education, Culture, Sports, Science and Technology, and the Grant-in-Aid for Nagoya University Global COE Program, \"Quest for Fundamental Principles in the Universe: from Particles to the Solar System and the Cosmos\". The work of S.G. is supported in part by DOE Grant DE-FG03-92-ER40701FG-02 and in part by NSF Grant PHY-0757647. The research of P.S. is supported by the DOE grant DE-FG03-92-ER40701FG-02, the European Commission under the Marie-Curie International Outgoing Fellowship Programme, and the Foundation for Polish Science. Opinions and conclusions expressed here are those of the authors and do not necessarily reflect the views of funding agencies.\n\nSubmitted - 1205.1515.pdf
", "abstract": "We introduce and compute a 2-parameter family deformation of the A-polynomial that encodes the color dependence of the superpolynomial and that, in suitable limits, reduces to various deformations of the A-polynomial studied in the literature. These special limits include the t-deformation which leads to the \"refined A-polynomial\" introduced in the previous work of the authors and the Q-deformation which leads, by the conjecture of Aganagic and Vafa, to the augmentation polynomial of knot contact homology. We also introduce and compute the quantum version of the super-A-polynomial, an operator that encodes recursion relations for S^r-colored HOMFLY homology. Much like its predecessor, the super-A-polynomial admits a simple physical interpretation as the defining equation for the space of SUSY vacua (= critical points of the twisted superpotential) in a circle compactification of the effective 3d N = 2 theory associated to a knot or, more generally, to a 3-manifold M. Equivalently, the algebraic curve defined by the zero locus of the super-A-polynomial can be thought of as the space of open string moduli in a brane system associated with M. As an inherent outcome of this work, we provide new interesting formulas for colored superpolynomials for the trefoil and the figure-eight knot.", "date": "2013-02-11", "date_type": "published", "publication": "Nuclear Physics B", "volume": "867", "number": "2", "publisher": "Elsevier", "pagerange": "506-546", "id_number": "CaltechAUTHORS:20130103-082610853", "issn": "0550-3213", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130103-082610853", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Ministry of Education, Culture, Sports, Science and Technology (MEXT)", "grant_number": "21740179" }, { "agency": "Nagoya University" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701FG-02" }, { "agency": "NSF", "grant_number": "PHY-0757647" }, { "agency": "Marie Curie Fellowship" }, { "agency": "Foundation for Polish Science" } ] }, "local_group": { "items": [ { "id": "Caltech-Theory" } ] }, "doi": "10.1016/j.nuclphysb.2012.10.005", "primary_object": { "basename": "1205.1515.pdf", "url": "https://authors.library.caltech.edu/records/70w97-98w52/files/1205.1515.pdf" }, "resource_type": "article", "pub_year": "2013", "author_list": "Fuji, Hiroyuki; Gukov, Sergei; et el." }, { "id": "https://authors.library.caltech.edu/records/3j4nr-btf78", "eprint_id": 37786, "eprint_status": "archive", "datestamp": "2023-08-22 08:06:54", "lastmod": "2023-10-23 18:03:39", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Fuji-Hiroyuki", "name": { "family": "Fuji", "given": "Hiroyuki" } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Sto\u0161i\u0107-M", "name": { "family": "Sto\u0161i\u0107", "given": "Marko" } }, { "id": "Su\u0142kowski-Piotr", "name": { "family": "Su\u0142kowski", "given": "Piotr" }, "orcid": "0000-0002-6176-6240" } ] }, "title": "3d analogs of Argyres-Douglas theories and knot homologies", "ispublished": "pub", "full_text_status": "public", "keywords": "Supersymmetric gauge theory; Duality in Gauge Field Theories; ChernSimons Theories; Differential and Algebraic Geometry", "note": "\u00a9 2013 Published for SISSA by Springer. This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. \n\nReceived: September 18, 2012; Accepted: December 23, 2012; Published: January 29, 2013. \n\nWe thank M. Aganagic, T. Dimofte, S. Nawata, L. Ng, V. Pestun, and C. Vafa for useful discussions. We also would like to thank the Institute for Theoretical Physics at University of Amsterdam (ITFA), Bethe Center for Theoretical Physics (BCTP) and Physikalisches Institut Universit\u00e4t in Bonn, the Simons Center for Geometry and Physics at Stony Brook, and Mathematical Sciences Center (MSC) of Tsinghua University for hospitality during\nvarious stages of this work. The work of H.F. is supported by the Grant-in-Aid for Young Scientists (B) [# 21740179] from the Japan Ministry of Education, Culture, Sports, Science and Technology, and the Grant-in-Aid for Nagoya University Global COE Program, \"Quest for Fundamental Principles in the Universe: from Particles to the Solar System and the Cosmos.\" The work of S.G. is supported in part by DOE Grant DE-FG03-92-ER40701FG-02 and in part by NSF Grant PHY-0757647. The work of M.S. is partially supported by Portuguese funds via the FCT - Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia, through project number PTDC/MAT/101503/2008, New Geometry and Topology. M.S. is also\npartially supported by the Ministry of Science of Serbia, project no. 174012. The research of P.S. is supported by the European Commission under the Marie-Curie International\nOutgoing Fellowship Programme and the Foundation for Polish Science. Opinions and conclusions expressed here are those of the authors and do not necessarily reflect the views\nof funding agencies.\n\nPublished - Fuji_2013p175.pdf
Submitted - 1209.1416v1.pdf
", "abstract": "We study singularities of algebraic curves associated with 3d N=2 theories that have at least one global flavor symmetry. Of particular interest is a class of theories T_K labeled by knots, whose partition functions package Poincar\u00e9 polynomials of the S^r -colored HOMFLY homologies. We derive the defining equation, called the super-A-polynomial, for algebraic curves associated with many new examples of 3d N=2 theories T K and study its singularity structure. In particular, we catalog general types of singularities that presumably exist for all knots and propose their physical interpretation. A computation of super-A-polynomials is based on a derivation of corresponding superpolynomials, which is interesting in its own right and relies solely on a structure of differentials in S^r -colored HOMFLY homologies.", "date": "2013-01", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2013", "number": "1", "publisher": "Springer", "pagerange": "Art. No. 175", "id_number": "CaltechAUTHORS:20130405-104147281", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130405-104147281", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Ministry of Education, Culture, Sports, Science and Technology (MEXT)", "grant_number": "21740179" }, { "agency": "Nagoya University Global COE Program" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701FG-02" }, { "agency": "NSF", "grant_number": "PHY-0757647" }, { "agency": "Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia (FCT)", "grant_number": "PTDC/MAT/101503/2008" }, { "agency": "Ministry of Science of Serbia", "grant_number": "174012" }, { "agency": "Marie Curie International Outgoing Fellowship" }, { "agency": "Foundation for Polish Science" } ] }, "local_group": { "items": [ { "id": "Caltech-Theory" } ] }, "doi": "10.1007/JHEP01(2013)175", "primary_object": { "basename": "1209.1416v1.pdf", "url": "https://authors.library.caltech.edu/records/3j4nr-btf78/files/1209.1416v1.pdf" }, "related_objects": [ { "basename": "Fuji_2013p175.pdf", "url": "https://authors.library.caltech.edu/records/3j4nr-btf78/files/Fuji_2013p175.pdf" } ], "resource_type": "article", "pub_year": "2013", "author_list": "Fuji, Hiroyuki; Gukov, Sergei; et el." }, { "id": "https://authors.library.caltech.edu/records/6c9yk-x1577", "eprint_id": 46170, "eprint_status": "archive", "datestamp": "2023-08-19 14:03:30", "lastmod": "2023-10-26 19:33:26", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Dimofte-T-D", "name": { "family": "Dimofte", "given": "Tudor" } }, { "id": "Gaiotto-D", "name": { "family": "Gaiotto", "given": "Davide" } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" } ] }, "title": "3-Manifolds and 3d indices", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2013 International Press.\n\nWe would like to thank Christopher Beem, Abhijit Gadde, Daniel Green,\nAnton Kapustin, Sara Pasquetti, Leonardo Rastelli, Schlomo Razamat,\nNathan Seiberg, Cumrun Vafa, Roland van der Veen, and Edward Witten\nfor illuminating discussions. The work of TD is supported primarily by\nthe Friends of the Institute for Advanced Study, and in part by DOE grant\nDE-FG02-90ER40542. The work of DG is supported in part by NSF grant\nPHY-0503584 and in part by the Roger Dashen membership in the Institute\nfor Advanced Study. The work of SG is supported in part by DOE Grant\nDE-FG03-92-ER40701 and in part by NSF Grant PHY-0757647. TD and\nSG thank the Simons Center for Geometry and Physics for their hospitality\nduring the Simons Workshop in Mathematics and Physics, 2011, where\npart of this work was initiated. Opinions and conclusions expressed here\nare those of the authors and do not necessarily reflect the views of funding\nagencies.\n\nPublished - ATMP-2013-0017-0005-a003.pdf
Submitted - 1112.5179v1.pdf
", "abstract": "We identify a large class R of three-dimensional N = 2 superconformal\nfield theories. This class includes the effective theories T_M of M5-branes\nwrapped on 3-manifolds M, discussed in previous work by the authors,\nand more generally comprises theories that admit a UV description as\nabelian Chern\u2013Simons-matter theories with (possibly non-perturbative)\nsuperpotential. Mathematically, class R might be viewed as an extreme\nquantum generalization of the Bloch group; in particular, the equivalence\nrelation among theories in class R is a quantum-field-theoretic \"2 to 3\nmove.\" We proceed to study the supersymmetric index of theories in\nclass R, uncovering its physical and mathematical properties, including\nrelations to algebras of line operators and to 4d indices. For 3-manifold\ntheories T_M, the index is a new topological invariant, which turns out to\nbe equivalent to non-holomorphic SL(2,\u2102) Chern\u2013Simons theory on M\nwith a previously unexplored \"integration cycle.\"", "date": "2013", "date_type": "published", "publication": "Advances in Theoretical and Mathematical Physics", "volume": "17", "number": "5", "publisher": "International Press", "pagerange": "975-1076", "id_number": "CaltechAUTHORS:20140610-081020607", "issn": "1095-0761", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20140610-081020607", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Friends of the Institute for Advanced Study" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG02-90ER40542" }, { "agency": "NSF", "grant_number": "PHY-0503584" }, { "agency": "Institute for Advanced Study" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" }, { "agency": "NSF", "grant_number": "PHY-0757647" } ] }, "local_group": { "items": [ { "id": "Caltech-Theory" } ] }, "doi": "10.4310/ATMP.2013.v17.n5.a3", "primary_object": { "basename": "1112.5179v1.pdf", "url": "https://authors.library.caltech.edu/records/6c9yk-x1577/files/1112.5179v1.pdf" }, "related_objects": [ { "basename": "ATMP-2013-0017-0005-a003.pdf", "url": "https://authors.library.caltech.edu/records/6c9yk-x1577/files/ATMP-2013-0017-0005-a003.pdf" } ], "resource_type": "article", "pub_year": "2013", "author_list": "Dimofte, Tudor; Gaiotto, Davide; et el." }, { "id": "https://authors.library.caltech.edu/records/2dtqs-sey14", "eprint_id": 31436, "eprint_status": "archive", "datestamp": "2023-08-22 04:52:12", "lastmod": "2023-10-17 16:35:14", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Su\u0142kowski-Piotr", "name": { "family": "Su\u0142kowski", "given": "Piotr" }, "orcid": "0000-0002-6176-6240" } ] }, "title": "A-polynomial, B-model, and quantization", "ispublished": "pub", "full_text_status": "public", "keywords": "Matrix Models; Non-Commutative Geometry; Chern-Simons Theories; Topological Strings", "note": "\u00a9 2012 Springer, Part of Springer Science+Business Media.\nPublished for SISSA by Springer.\nThis article is distributed under the terms of the Creative Commons\nAttribution License which permits any use, distribution and reproduction in any medium,\nprovided the original author(s) and source are credited.\nReceived: November 2, 2011; accepted: January 31, 2012; published: February 20, 2012.\n\nIt is pleasure to thank Vincent Bouchard, Tudor Dimofte, Nathan Dunfield, Bertrand\nEynard, Maxim Kontsevich, and Don Zagier for helpful discussions and correspondence.\nThe work of S.G. is supported in part by DOE Grant DE-FG03-92-ER40701FG-02 and\nin part by NSF Grant PHY-0757647. The research of P.S. is supported by the DOE\ngrant DE-FG03-92-ER40701FG-02 and the European Commission under the Marie-Curie\nInternational Outgoing Fellowship Programme. Opinions and conclusions expressed here\nare those of the authors and do not necessarily reflect the views of funding agencies.\n\nPublished - Gukov2012p18084J_High_Energy_Phys.pdf
", "abstract": "Exact solution to many problems in mathematical physics and quantum field theory often can be expressed in terms of an algebraic curve equipped with a meromorphic differential. Typically, the geometry of the curve can be seen most clearly in a suitable semi-classical limit, as \u0127 \u2192 0, and becomes non-commutative or \"quantum\" away from this limit. For a classical curve defined by the zero locus of a polynomial A(x, y), we provide a construction of its non-commutative counterpart \u00c2(^x, ^y) using the technique of the topological recursion. This leads to a powerful and systematic algorithm for computing \u00c2 that, surprisingly, turns out to be much simpler than any of the existent methods. In particular, as a bonus feature of our approach comes a curious observation that, for all curves that come from knots or topological strings, their non-commutative counterparts can be determined just from the first few steps of the topological recursion. We also propose a Ktheory criterion for a curve to be \"quantizable,\" and then apply our construction to many examples that come from applications to knots, strings, instantons, and random matrices.", "date": "2012-02", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2012", "number": "2", "publisher": "Springer", "pagerange": "Art. No. 070", "id_number": "CaltechAUTHORS:20120511-113608838", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120511-113608838", "rights": "This article is distributed under the terms of the Creative Commons\nAttribution License which permits any use, distribution and reproduction in any medium,\nprovided the original author(s) and source are credited.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701FG-02" }, { "agency": "NSF", "grant_number": "PHY-0757647" }, { "agency": "Marie Curie Fellowship" } ] }, "local_group": { "items": [ { "id": "Caltech-Theory" } ] }, "doi": "10.1007/JHEP02(2012)070", "primary_object": { "basename": "Gukov2012p18084J_High_Energy_Phys.pdf", "url": "https://authors.library.caltech.edu/records/2dtqs-sey14/files/Gukov2012p18084J_High_Energy_Phys.pdf" }, "resource_type": "article", "pub_year": "2012", "author_list": "Gukov, Sergei and Su\u0142kowski, Piotr" }, { "id": "https://authors.library.caltech.edu/records/853k8-bb920", "eprint_id": 39761, "eprint_status": "archive", "datestamp": "2023-08-19 09:15:31", "lastmod": "2023-10-24 17:10:12", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Fuji-Hiroyuki", "name": { "family": "Fuji", "given": "Hiroyuki" } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Su\u0142kowski-Piotr", "name": { "family": "Su\u0142kowski", "given": "Piotr" }, "orcid": "0000-0002-6176-6240" }, { "id": "Awata-Hidetoshi", "name": { "family": "Awata", "given": "Hidetoshi" } } ] }, "title": "Volume conjecture: refined and categorified", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2012 International Press.\n\nWe thank H.-J. Chung and R.H. Dijkgraaf for useful discussions during the early stages of this work. We thank M. Aganagic, A. Iqbal, D. Krefl, and Sh. Shakirov for discussions and comments. The authors would also like to\nthank the following institutions for their hospitality: California Institute of Technology (H.F.), the Banff International Research Station (H.F., P.S.), and the Simons Center for Geometry and Physics (H.F., S.G., P.S.). The\nwork of H.F. is supported by the Grant-in-Aid for Young Scientists (B) [#21740179] from the Japan Ministry of Education, Culture, Sports, Science and Technology, and the Grant-in-Aid for Nagoya University Global COE Program, \"Quest for Fundamental Principles in the Universe: from Particles to the Solar System and the Cosmos.\" The work of S.G. is supported in part by DOE Grant DE-FG03-92-ER40701FG-02 and in part by NSF Grant PHY-0757647. The research of P.S. is supported by the DOE grant\nDE-FG03-92-ER40701FG-02, the European Commission under the Marie-Curie International Outgoing Fellowship Programme, and the Foundation for Polish Science. Opinions and conclusions expressed here are those of the authors and do not necessarily reflect the views of funding agencies.\n\nPublished - ATMP-2012-0016-0006-00026542.pdf
Submitted - 1203.2182v1.pdf
", "abstract": "The generalized volume conjecture relates asymptotic behavior of the colored Jones polynomials to objects naturally defined on an algebraic curve, the zero locus of the A-polynomial A(x,y). Another \"family version\" of the volume conjecture depends on a quantization parameter, usually denoted q or \u0127; this quantum volume conjecture (also known as the AJ-conjecture) can be stated in a form of a q-difference equation that annihilates the colored Jones polynomials and SL(2,C) Chern\u2013 Simons partition functions. We propose refinements/categorifications of both conjectures that include an extra deformation parameter t and describe similar properties of homological knot invariants and refined BPS invariants. Much like their unrefined/decategorified predecessors, that correspond to t=\u22121, the new volume conjectures involve objects naturally defined on an algebraic curve A^(ref)(x,y;t) obtained by a particular deformation of the A-polynomial, and its quantization \u00c2^(ref)(x\u02c6,\u0177;q,t). We compute both classical and quantum t-deformed curves in a number of examples coming from colored knot homologies and refined BPS invariants.", "date": "2012", "date_type": "published", "publication": "Advances in Theoretical and Mathematical Physics", "volume": "16", "number": "6", "publisher": "International Press", "pagerange": "1669-1777", "id_number": "CaltechAUTHORS:20130805-101410619", "issn": "1095-0761", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130805-101410619", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Ministry of Education, Culture, Sports, Science and Technology (MEXT)", "grant_number": "21740179" }, { "agency": "Nagoya University" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701FG-02" }, { "agency": "NSF", "grant_number": "PHY-0757647" }, { "agency": "Marie Curie Fellowship" }, { "agency": "Foundation for Polish Science" } ] }, "doi": "10.48550/arXiv.1203.2182", "primary_object": { "basename": "1203.2182v1.pdf", "url": "https://authors.library.caltech.edu/records/853k8-bb920/files/1203.2182v1.pdf" }, "related_objects": [ { "basename": "ATMP-2012-0016-0006-00026542.pdf", "url": "https://authors.library.caltech.edu/records/853k8-bb920/files/ATMP-2012-0016-0006-00026542.pdf" } ], "resource_type": "article", "pub_year": "2012", "author_list": "Fuji, Hiroyuki; Gukov, Sergei; et el." }, { "id": "https://authors.library.caltech.edu/records/6zq6y-a4z78", "eprint_id": 28768, "eprint_status": "archive", "datestamp": "2023-08-19 08:45:22", "lastmod": "2023-10-24 18:08:38", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" } ] }, "title": "Quantization via mirror symmetry", "ispublished": "pub", "full_text_status": "public", "keywords": "mirror symmetry, derived category, branes, quantization, symplectic geometry", "note": "\u00a9 2011 The Mathematical Society of Japan and Springer. \n\nReceived: 5 November 2010; Revised: 1 November 2011; Accepted: 8 November 2011. Published online: 25 December 2011. \n\nThis article is based on the 8th Takagi Lectures that the author delivered at Research Institute for Mathematical Sciences, Kyoto University on November 23, 2010. I would like to thank the organizing committee of the Takagi Lectures for inviting me, and to acknowledge helpful discussions with E. Frenkel, T. Hausel, and E. Witten.\nI also would like to thank E. Witten for collaboration on the A-model approach to quantization reviewed in Section 2. Special thanks are in order to referees for careful reading of the manuscript and suggesting many useful improvements.\nThis work is supported in part by DOE Grant DE-FG03-92-ER40701 and in part by NSF Grant PHY-0757647. Opinions and conclusions expressed here are those of the author and do not necessarily reflect the views of funding agencies.\n\nSubmitted - 1011.2218v2.pdf
", "abstract": "When combined with mirror symmetry, the A-model approach to quantization leads to a fairly simple and tractable problem. The most interesting part of the problem then becomes finding the mirror of the coisotropic brane. We illustrate how it can be addressed in a number of\ninteresting examples related to representation theory and gauge theory, in which mirror geometry is naturally associated with the Langlands dual group. Hyperholomorphic sheaves and (B, B, B) branes play an important role in the B-model approach to quantization.", "date": "2011-12", "date_type": "published", "publication": "Japanese Journal of Mathematics", "volume": "6", "number": "2", "publisher": "Springer", "pagerange": "65-119", "id_number": "CaltechAUTHORS:20120113-091504097", "issn": "0289-2316", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120113-091504097", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" }, { "agency": "NSF", "grant_number": "PHY-0757647" } ] }, "local_group": { "items": [ { "id": "Caltech-Theory" } ] }, "doi": "10.1007/s11537-011-1033-2", "primary_object": { "basename": "1011.2218v2.pdf", "url": "https://authors.library.caltech.edu/records/6zq6y-a4z78/files/1011.2218v2.pdf" }, "resource_type": "article", "pub_year": "2011", "author_list": "Gukov, Sergei" }, { "id": "https://authors.library.caltech.edu/records/fxgbh-qhn04", "eprint_id": 28396, "eprint_status": "archive", "datestamp": "2023-08-22 04:12:46", "lastmod": "2023-10-24 17:51:46", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Dimofte-T-D", "name": { "family": "Dimofte", "given": "Tudor" } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Hollands-L", "name": { "family": "Hollands", "given": "Lotte" } } ] }, "title": "Vortex Counting and Lagrangian 3-Manifolds", "ispublished": "pub", "full_text_status": "public", "keywords": "gauge theory; vortex equations; BPS invariants; D-branes; conformal field theory", "note": "\u00a9 2011 Springer. \n\nReceived: 3 March 2011; Revised: 30 August 2011; Accepted: 9 September 2011. Published online: 5 October 2011. \n\nWe would like to thank M. Aganagic, C. Beem, A. Borodin, A. Braverman, A. Gorsky, C. Keller, H. Nakajima, J. Song, and E. Witten for very useful discussions, and C. Vafa for collaboration at an earlier stage of this project. The work of SG and LH is supported in part by NSF grant PHY-0757647. The work of SG\nis also supported in part by DOE grant DE-FG03-92-ER40701 and in part by the Alfred P. Sloan Foundation. Opinions and conclusions expressed here are those of the authors and do not necessarily reflect the views of funding agencies.\n\nSubmitted - 1006.0977v1.pdf
", "abstract": "To every 3-manifold M one can associate a two-dimensional N=(2,2) supersymmetric field theory by compactifying five-dimensional N=2 super-Yang\u2013Mills theory on M. This system naturally appears in the study of half-BPS surface operators in four-dimensional N=2 gauge theories on one hand, and in the geometric approach to knot homologies, on the other. We study the relation between vortex counting in such two-dimensional N=(2,2) supersymmetric field theories and the refined BPS invariants of the dual geometries. In certain cases, this counting can also be mapped to the computation of degenerate conformal blocks in two-dimensional CFT's. Degenerate limits of vertex operators\nin CFT receive a simple interpretation via geometric transitions in BPS counting.", "date": "2011-12", "date_type": "published", "publication": "Letters in Mathematical Physics", "volume": "98", "number": "3", "publisher": "Springer", "pagerange": "225-287", "id_number": "CaltechAUTHORS:20111209-105547167", "issn": "0377-9017", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20111209-105547167", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-0757647" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" }, { "agency": "Alfred P. Sloan Foundation" } ] }, "local_group": { "items": [ { "id": "Caltech-Theory" } ] }, "doi": "10.1007/s11005-011-0531-8", "primary_object": { "basename": "1006.0977v1.pdf", "url": "https://authors.library.caltech.edu/records/fxgbh-qhn04/files/1006.0977v1.pdf" }, "resource_type": "article", "pub_year": "2011", "author_list": "Dimofte, Tudor; Gukov, Sergei; et el." }, { "id": "https://authors.library.caltech.edu/records/kcpmw-sdn19", "eprint_id": 22923, "eprint_status": "archive", "datestamp": "2023-08-22 01:45:25", "lastmod": "2023-10-23 17:21:02", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Dimofte-T-D", "name": { "family": "Dimofte", "given": "Tudor" } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Soibelman-Y", "name": { "family": "Soibelman", "given": "Yan" } } ] }, "title": "Quantum Wall Crossing in N=2 Gauge Theories", "ispublished": "pub", "full_text_status": "public", "keywords": "motivic Donaldson-Thomas invariants; BPS invariants; wall-crossing; supersymmetric gauge theory", "note": "\u00a9 Springer 2010. \n\nReceived: 2 July 2010. Accepted: 20 September 2010. Published online: 16 October 2010. \n\nWe would like to thank D. Jafferis, M. Kontsevich, A. Neitzke, and M. Reineke for very useful discussions, and S. Deser and C. Silberstein for providing important clues. The work of SG is supported in part by DOE Grant DE-FG03-92-ER40701, in part by NSF Grant PHY-0757647, and in part by the Alfred P. Sloan Foundation. Y.S. is grateful to IHES for excellent research conditions. His work was partially supported by an NSF grant. Opinions and conclusions expressed here are those of the authors and do not necessarily reflect the views of funding agencies.\n\nSubmitted - 0912.1346v1.pdf
", "abstract": "We study refined and motivic wall-crossing formulas in N = 2 supersymmetric gauge theories with SU(2) gauge group and N _f < 4 matter hypermultiplets in the fundamental representation. Such gauge theories provide an excellent testing ground for the conjecture that \"refined = motivic.\"", "date": "2011-01", "date_type": "published", "publication": "Letters in Mathematical Physics", "volume": "95", "number": "1", "publisher": "Springer", "pagerange": "1-25", "id_number": "CaltechAUTHORS:20110316-093514240", "issn": "0377-9017", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110316-093514240", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" }, { "agency": "NSF", "grant_number": "PHY-0757647" }, { "agency": "Alfred P. Sloan Foundation" } ] }, "local_group": { "items": [ { "id": "Caltech-Theory" } ] }, "doi": "10.1007/s11005-010-0437-x", "primary_object": { "basename": "0912.1346v1.pdf", "url": "https://authors.library.caltech.edu/records/kcpmw-sdn19/files/0912.1346v1.pdf" }, "resource_type": "article", "pub_year": "2011", "author_list": "Dimofte, Tudor; Gukov, Sergei; et el." }, { "id": "https://authors.library.caltech.edu/records/xt2ry-nbk16", "eprint_id": 66693, "eprint_status": "archive", "datestamp": "2023-08-19 02:16:25", "lastmod": "2023-10-18 18:42:43", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Iqbal-A", "name": { "family": "Iqbal", "given": "Amer" } }, { "id": "Koz\u00e7az-C", "name": { "family": "Koz\u00e7az", "given": "Can" } }, { "id": "Vafa-C", "name": { "family": "Vafa", "given": "Cumrun" } } ] }, "title": "Link Homologies and the Refined Topological Vertex", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 The Author(s) 2010. This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited. \n\nReceived: 16 September 2009. Accepted: 14 December 2009. Published online: 20 April 2010. \n\nCommunicated by N.A. Nekrasov. \n\nWe would like to thank C. Doran, J. Rasmussen, and B.Webster for valuable discussions. It is our pleasure to thank the Stony Brook physics department and the 4th Simons Workshop in Mathematics and Physics for hospitality during the initial stages of this work. In addition, C.V. thanks the CTP at MIT for hospitality during his sabbatical leave. The work of S.G. is supported in part by DOE grant DE-FG03-92-ER40701, in part by RFBR grant 04-02-16880, and in part by the grant for support of scientific schools NSh-8004.2006.2. The work of C.V. is supported in part by NSF grants PHY-0244821 and DMS-0244464.\n\nPublished - Gukov,S.757-.pdf
Submitted - 0705.1368.pdf
", "abstract": "We establish a direct map between refined topological vertex and sl(N) homological invariants of the of Hopf link, which include Khovanov-Rozansky homology as a special case. This relation provides an exact answer for homological invariants of the Hopf link, whose components are colored by arbitrary representations of sl(N). At present, the mathematical formulation of such homological invariants is available only for the fundamental representation (the Khovanov-Rozansky theory) and the relation with the refined topological vertex should be useful for categorizing quantum group invariants associated with other representations (R _1, R _2). Our result is a first direct verification of a series of conjectures which identifies link homologies with the Hilbert space of BPS states in the presence of branes, where the physical interpretation of gradings is in terms of charges of the branes ending on Lagrangian branes.", "date": "2010-04-20", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "298", "number": "3", "publisher": "Springer", "pagerange": "757-785", "id_number": "CaltechAUTHORS:20160505-114729379", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160505-114729379", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" }, { "agency": "Russian Foundation for Basic Research (RFBR)", "grant_number": "04-02-16880" }, { "agency": "NSF", "grant_number": "PHY-0244821" }, { "agency": "NSF", "grant_number": "DMS-0244464" } ] }, "doi": "10.1007/s00220-010-1045-4", "primary_object": { "basename": "0705.1368.pdf", "url": "https://authors.library.caltech.edu/records/xt2ry-nbk16/files/0705.1368.pdf" }, "related_objects": [ { "basename": "Gukov,S.757-.pdf", "url": "https://authors.library.caltech.edu/records/xt2ry-nbk16/files/Gukov,S.757-.pdf" } ], "resource_type": "article", "pub_year": "2010", "author_list": "Gukov, Sergei; Iqbal, Amer; et el." }, { "id": "https://authors.library.caltech.edu/records/4q3k7-mjj66", "eprint_id": 17582, "eprint_status": "archive", "datestamp": "2023-08-21 23:09:10", "lastmod": "2023-10-20 00:01:31", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Alday-L-F", "name": { "family": "Alday", "given": "Luis F." } }, { "id": "Gaiotto-D", "name": { "family": "Gaiotto", "given": "Davide" } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Tachikawa-Yuji", "name": { "family": "Tachikawa", "given": "Yuji" } }, { "id": "Verlinde-H", "name": { "family": "Verlinde", "given": "Herman" } } ] }, "title": "Loop and surface operators in N = 2 gauge theory and Liouville modular geometry", "ispublished": "pub", "full_text_status": "public", "keywords": "Supersymmetry and Duality; Conformal and W Symmetry; Supersymmetric gauge theory", "note": "\u00a9 2010 Springer. Published for SISSA by Springer. This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited. \n\nReceived: 31 October 2009. Accepted: 6 January 2010. Published online: 27 January 2010. \n\nWe have benefited from useful discussions with N. Drukker, J. Gomis, J. Maldacena, N.\nNekrasov, T. Okuda, V. Pestun, N. Seiberg, J. Teschner, C. Vafa, E. Verlinde, and E.\nWitten. L.F.A. and D.G. are supported in part by the DOE grant DE-FG02- 90ER40542.\nD.G. is supported in part by the Roger Dashen membership in the Institute for Advanced\nStudy. YT is supported in part by the NSF grant PHY-0503584, and by the Marvin L.\nGoldberger membership at the Institute for Advanced Study. The research of H.V. is\nsupported by the National Science Foundation under Grant No. PHY-0756966 and by an\nEinstein Fellowship of the Institute for Advanced Study. The work of SG is supported in\npart by DOE grant DE-FG03-92-ER40701, in part by NSF grant PHY07-57647, and in\npart by the Alfred P. Sloan Foundation. Opinions and conclusions expressed here are those\nof the authors and do not necessarily reflect the views of funding agencies.\n\nPublished - Alday2010p7111J_High_Energy_Phys.pdf
", "abstract": "Recently, a duality between Liouville theory and four dimensional N = 2 gauge theory has been uncovered by some of the authors. We consider the role of extended objects in gauge theory, surface operators and line operators, under this correspondence. We map such objects to specific operators in Liouville theory. We employ this connection to compute the expectation value of general supersymmetric 't Hooft-Wilson line operators in a variety of N = 2 gauge theories.", "date": "2010-01", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2010", "number": "1", "publisher": "Springer", "pagerange": "Art. No. 113", "id_number": "CaltechAUTHORS:20100224-150755870", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20100224-150755870", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG02- 90ER40542" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" }, { "agency": "Institute for Advanced Study" }, { "agency": "NSF", "grant_number": "PHY-0503584" }, { "agency": "NSF", "grant_number": "PHY-0757647" }, { "agency": "NSF", "grant_number": "PHY-0756966" }, { "agency": "Alfred P. Sloan Foundation" } ] }, "local_group": { "items": [ { "id": "Caltech-Theory" } ] }, "doi": "10.1007/JHEP01(2010)113", "primary_object": { "basename": "Alday2010p7111J_High_Energy_Phys.pdf", "url": "https://authors.library.caltech.edu/records/4q3k7-mjj66/files/Alday2010p7111J_High_Energy_Phys.pdf" }, "resource_type": "article", "pub_year": "2010", "author_list": "Alday, Luis F.; Gaiotto, Davide; et el." }, { "id": "https://authors.library.caltech.edu/records/513j8-7az43", "eprint_id": 17050, "eprint_status": "archive", "datestamp": "2023-08-21 23:05:25", "lastmod": "2023-10-19 22:46:01", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Dimofte-T-D", "name": { "family": "Dimofte", "given": "Tudor" } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" } ] }, "title": "Refined, Motivic, and Quantum", "ispublished": "pub", "full_text_status": "public", "keywords": "motivic Donaldson\u2013Thomas invariants; D-branes, BPS invariants; wall-crossing; three-dimensional partitions", "note": "\u00a9 2009 Springer. \n\nReceived: 17 June 2009; accepted: 16 September 2009; published online: 14 November 2009. \n\nWe thank A. Gorsky, E. Gorsky, D. Jafferis, G. Moore, A. Neitzke, H. Ooguri,\nY. Soibelman, and M. Yamazaki for useful discussions and comments. We are\ngrateful to the KITP, Santa Barbara for warm hospitality during the program\n\"Fundamental Aspects of Superstring Theory,\" where part of this work was carried\nout. TD acknowledges support from a National Defense Science and Engineering\nGraduate Fellowship. Research of SG is supported in part by the Alfred\nP. Sloan Foundation, by DARPA under Grant No. HR0011-09-1-0015, and by\nthe National Science Foundation under Grant No. PHY05-51164 and Grant No.\nPHY07-57647. Opinions and conclusions expressed here are those of the authors\nand do not necessarily reflect the views of funding agencies.\n\nSubmitted - 0904.1420v1.pdf
", "abstract": "It is well known that in string compactifications on toric Calabi\u2013Yau manifolds one can introduce refined BPS invariants that carry information not only about the charge of the BPS state but also about the spin content. In this paper we study how these invariants behave under wall crossing. In particular, by applying a refined wall crossing formula, we obtain the refined BPS degeneracies for the conifold in different chambers. The result can be interpreted in terms of a new statistical model that counts \"refined\" pyramid partitions; the model provides a combinatorial realization of wall crossing and clarifies the relation between refined pyramid partitions and the refined topological vertex. We also compare the wall crossing behavior of the refined BPS invariants with that of the motivic Donaldson\u2013Thomas invariants introduced by Kontsevich\u2013Soibelman. In particular, we argue that, in the context of BPS state counting, the three adjectives in the title of this paper are essentially synonymous.", "date": "2010-01", "date_type": "published", "publication": "Letters in Mathematical Physics", "volume": "91", "number": "1", "publisher": "Springer", "pagerange": "1-27", "id_number": "CaltechAUTHORS:20100104-122110812", "issn": "0377-9017", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20100104-122110812", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "National Defense Science and Engineering Graduate (NDSEG) Fellowship" }, { "agency": "Alfred P. Sloan Foundation" }, { "agency": "Defense Advanced Research Projects Agency (DARPA)", "grant_number": "HR0011-09-1-0015" }, { "agency": "NSF", "grant_number": "PHY-0551164" }, { "agency": "NSF", "grant_number": "PHY-0757647" } ] }, "other_numbering_system": { "items": [ { "id": "68-2725", "name": "CALT" } ] }, "local_group": { "items": [ { "id": "Caltech-Theory" } ] }, "doi": "10.1007/s11005-009-0357-9", "primary_object": { "basename": "0904.1420v1.pdf", "url": "https://authors.library.caltech.edu/records/513j8-7az43/files/0904.1420v1.pdf" }, "resource_type": "article", "pub_year": "2010", "author_list": "Dimofte, Tudor and Gukov, Sergei" }, { "id": "https://authors.library.caltech.edu/records/fvwqv-cbd70", "eprint_id": 66644, "eprint_status": "archive", "datestamp": "2023-08-19 01:19:21", "lastmod": "2023-10-18 18:39:41", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Witten-E", "name": { "family": "Witten", "given": "Edward" }, "orcid": "0000-0002-7752-6073" } ] }, "title": "Rigid Surface Operators", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2010 International Press. \n\nWe would like to thank R. Bezrukavnikov, A. Braverman, A. Elashvili, D. Gaiotto, V. Kac, G. Lusztig, C. Vafa, and especially D. Kazhdan for valuable discussions and correspondence. Research of SG is supported in part by NSF Grant DMS-0635607, in part by RFBR grant 07-02-00645, and in part by the Alfred P. Sloan Foundation. Research of EW is partly supported by NSF Grant PHY-0503584. Conclusions reported here are those of the authors and not of funding agencies.\n\nPublished - euclid.atmp.1283281759.pdf
Submitted - 0804.1561.pdf
", "abstract": "Surface operators in gauge theory are analogous to Wilson and 't Hooft line operators except that they are supported on a two-dimensional surface rather than a one-dimensional curve. In a previous paper, we constructed a certain class of half-BPS surface operators in N = 4 super Yang\u2013Mills theory, and determined how they transform under S-duality. Those surface operators depend on a relatively large number of freely adjustable parameters. In the present paper, we consider the opposite case of half-BPS surface operators that are \"rigid\" in the sense that they do not depend on any parameters at all. We present some simple constructions of rigid half-BPS surface operators and attempt to determine how they transform under duality. This attempt is only partially successful, suggesting that our constructions are not the whole story. The partial match suggests interesting connections with quantization. We discuss some possible refinements and some string theory constructions which might lead to a more complete picture.", "date": "2010-01", "date_type": "published", "publication": "Advances in Theoretical and Mathematical Physics", "volume": "14", "number": "1", "publisher": "International Press", "pagerange": "87-178", "id_number": "CaltechAUTHORS:20160504-103840382", "issn": "1095-0761", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160504-103840382", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0635607" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "07-02-00645" }, { "agency": "Alfred P. Sloan Foundation" }, { "agency": "NSF", "grant_number": "PHY-0503584" } ] }, "collection": "CaltechAUTHORS", "doi": "10.4310/ATMP.2010.v14.n1.a3", "primary_object": { "basename": "0804.1561.pdf", "url": "https://authors.library.caltech.edu/records/fvwqv-cbd70/files/0804.1561.pdf" }, "related_objects": [ { "basename": "euclid.atmp.1283281759.pdf", "url": "https://authors.library.caltech.edu/records/fvwqv-cbd70/files/euclid.atmp.1283281759.pdf" } ], "resource_type": "article", "pub_year": "2010", "author_list": "Gukov, Sergei and Witten, Edward" }, { "id": "https://authors.library.caltech.edu/records/t780d-xyj74", "eprint_id": 20708, "eprint_status": "archive", "datestamp": "2023-08-19 00:14:11", "lastmod": "2023-10-20 23:21:08", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Witten-E", "name": { "family": "Witten", "given": "Edward" }, "orcid": "0000-0002-7752-6073" } ] }, "title": "Branes and quantization", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2009 International Press.\n\nWe would like to thank D. Kazhdan, M. Kontsevich, N. Hitchin, and P. Sarnak for valuable discussions. Research of SG is supported in part by NSF Grants DMS-0635607 and PHY-0757647, in part by RFBR grant 07-02-00645, and in part by the Alfred P. Sloan Foundation. Research of EW is\nsupported in part by NSF Grant PHY-0503584. Conclusions reported here are those of the authors and not of funding agencies.\n\nPublished - Gukov2009p11796Adv_Theor_Math_Phys.pdf
", "abstract": "The problem of quantizing a symplectic manifold (M,\u03c9) can be formulated in terms of the A-model of a complexification of M. This leads to an interesting new perspective on quantization. From this point of view, the Hilbert space obtained by quantization of (M,\u03c9) is the space of (B_(cc), B) strings, where B_(cc) and B are two A-branes; B is an ordinary Lagrangian A-brane, and Bcc is a space-filling coisotropic A-brane. B is supported on M, and the choice of \u03c9 is encoded in the choice of B_(cc). As an example, we describe from this point of view the representations of the\ngroup SL(2,R). Another application is to Chern\u2013Simons gauge theory.", "date": "2009-10", "date_type": "published", "publication": "Advances in Theoretical and Mathematical Physics", "volume": "13", "number": "5", "publisher": "International Press", "pagerange": "1445-1518", "id_number": "CaltechAUTHORS:20101108-100406383", "issn": "1095-0761", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20101108-100406383", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0635607" }, { "agency": "NSF", "grant_number": "PHY-0757647" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "07- 02-00645" }, { "agency": "Alfred P. Sloan Foundation" }, { "agency": "NSF", "grant_number": "PHY-0503584" } ] }, "doi": "10.4310/ATMP.2009.v13.n5.a5", "primary_object": { "basename": "Gukov2009p11796Adv_Theor_Math_Phys.pdf", "url": "https://authors.library.caltech.edu/records/t780d-xyj74/files/Gukov2009p11796Adv_Theor_Math_Phys.pdf" }, "resource_type": "article", "pub_year": "2009", "author_list": "Gukov, Sergei and Witten, Edward" }, { "id": "https://authors.library.caltech.edu/records/y1pmt-j1802", "eprint_id": 17372, "eprint_status": "archive", "datestamp": "2023-08-20 00:18:04", "lastmod": "2023-10-19 23:49:47", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Dimofte-T-D", "name": { "family": "Dimofte", "given": "Tudor" } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Lenells-J", "name": { "family": "Lenells", "given": "Jonatan" } }, { "id": "Zagier-D", "name": { "family": "Zagier", "given": "Don" } } ] }, "title": "Exact Results for Perturbative Chern-Simons Theory with Complex Gauge Group", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2009 International Press. \n\nReceived March 18, 2009. \n\nWe would like to thank D. Auroux, N. Dunfield, S. Garoufalidis, K. Hikami, T. Mrowka,\nW. Neumann, E. Witten, and C. Zickert for useful discussions and correspondence. Research\nof SG is supported in part by NSF Grant PHY-0757647 and in part by the Alfred P.\nSloan Foundation. JL acknowledges support from a Marie Curie Intra-European Fellowship.\nTD acknowledges support from a National Defense Science and Engineering Graduate\nFellowship. Opinions and conclusions expressed here are those of the authors and do not\nnecessarily reflect the views of funding agencies.\n\nPublished - Dimofte2009p6866Commun._Number_Theory_Phys.pdf
", "abstract": "We develop several methods that allow us to compute all-loop partition functions in perturbative Chern-Simons theory with complex gauge group G_C, sometimes\nin multiple ways. In the background of a non-abelian irreducible flat connection, perturbative G_C invariants turn out to be interesting topological invariants, which are very different from finite type (Vassiliev) invariants obtained in a theory with compact gauge group G. We explore various aspects of these invariants and present an example where we compute them explicitly to high loop order. We also introduce a notion of \"arithmetic TQFT\" and conjecture (with supporting numerical evidence) that SL(2,C) Chern-Simons theory is an example of such a theory.", "date": "2009", "date_type": "published", "publication": "Communications in Number Theory and Physics", "volume": "3", "number": "2", "publisher": "International Press", "pagerange": "363-443", "id_number": "CaltechAUTHORS:20100202-111957900", "issn": "1931-4523", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20100202-111957900", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-0757647" }, { "agency": "Alfred P. Sloan Foundation" }, { "agency": "Marie Curie Fellowship" }, { "agency": "National Defense Science and Engineering Graduate (NDSEG) Fellowship" } ] }, "doi": "10.4310/CNTP.2009.v3.n2.a4", "primary_object": { "basename": "Dimofte2009p6866Commun._Number_Theory_Phys.pdf", "url": "https://authors.library.caltech.edu/records/y1pmt-j1802/files/Dimofte2009p6866Commun._Number_Theory_Phys.pdf" }, "resource_type": "article", "pub_year": "2009", "author_list": "Dimofte, Tudor; Gukov, Sergei; et el." }, { "id": "https://authors.library.caltech.edu/records/sbjtp-jde45", "eprint_id": 66981, "eprint_status": "archive", "datestamp": "2023-08-20 00:06:36", "lastmod": "2023-10-18 19:49:22", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Murakami-Hitoshi", "name": { "family": "Murakami", "given": "Hitoshi" } } ] }, "title": "SL(2,C) Chern\u2013Simons Theory and the Asymptotic Behavior of the Colored Jones Polynomial", "ispublished": "pub", "full_text_status": "public", "keywords": "colored Jones polynomial, volume conjecture, A-polynomial, Chern\u2013Simons theory", "note": "\u00a9 2008 Springer. \n\nReceived: 7 July 2007; Revised: 18 August 2008; Accepted: 6 November 2008. \n\nThe authors would like to thank J\u00e9r\u00f4me Dubois, Stavros Garoufalidis, and Toshiaki Hattori for helpful conversations. It is also a pleasure to thank the organizers of the conference \"Around the Volume Conjecture\" at Columbia University in March 2006 and the conference \"Modular Forms and String Duality\" at Banff in June 2006, which stimulated much of this work. This work was supported in part by the DOE under grant number DE-FG03-92-ER40701, in part by RFBR grant 04-02-16880, and in part by the grant for support of scientific schools NSh-8004.2006.2 (S.G.), and in part by Grant-in-Aid for Scientific Research (B) (15340019) (H.M.).\n\nPublished - art_3A10.1007_2Fs11005-008-0282-3.pdf
Submitted - 0608324.pdf
", "abstract": "It has been proposed that the asymptotic behavior of the colored Jones polynomial is equal to the perturbative expansion of the Chern\u2013Simons gauge theory with complex gauge group SL(2,C) on the hyperbolic knot complement. In this note we make the first step toward verifying this relation beyond the semi-classical approximation. This requires a careful understanding of some delicate issues, such as normalization of the colored Jones polynomial and the choice of polarization in Chern\u2013Simons theory. Addressing these issues allows us to go beyond the volume conjecture and to verify some predictions for the behavior of the subleading terms in the asymptotic expansion of the colored Jones polynomial.", "date": "2008-12", "date_type": "published", "publication": "Letters in Mathematical Physics", "volume": "86", "number": "2-3", "publisher": "Springer", "pagerange": "79-98", "id_number": "CaltechAUTHORS:20160511-094807499", "issn": "0377-9017", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160511-094807499", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "04-02-16880" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "15340019" } ] }, "doi": "10.1007/s11005-008-0282-3", "primary_object": { "basename": "0608324.pdf", "url": "https://authors.library.caltech.edu/records/sbjtp-jde45/files/0608324.pdf" }, "related_objects": [ { "basename": "art_3A10.1007_2Fs11005-008-0282-3.pdf", "url": "https://authors.library.caltech.edu/records/sbjtp-jde45/files/art_3A10.1007_2Fs11005-008-0282-3.pdf" } ], "resource_type": "article", "pub_year": "2008", "author_list": "Gukov, Sergei and Murakami, Hitoshi" }, { "id": "https://authors.library.caltech.edu/records/js3z3-npm25", "eprint_id": 66982, "eprint_status": "archive", "datestamp": "2023-08-19 23:46:56", "lastmod": "2023-10-18 19:49:25", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Witten-E", "name": { "family": "Witten", "given": "Edward" }, "orcid": "0000-0002-7752-6073" } ] }, "title": "Gauge Theory, Ramification, And The Geometric Langlands Program", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2008 International Press. \n\nWe thank A. Braverman, D. Gaitsgory, E. Frenkel, and D. Kazhdan for patient and extremely helpful explanations. We also thank J. Andersen, P. Aspinwall, M. F. Atiyah, D. Ben-Zvi, R. Bezrukavnikov, R. Bielawski, R. Dijkgraaf, R. Donagi, N. Hitchin, L. Jeffrey, A. Kapustin, P. Kronheimer, Y. Laszlo, H. Nakajima, C. Sorger, and M. Thaddeus, among others, for a wide variety of helpful comments and advice. Research of SG was partly supported by DOE grant DE-FG03-92-ER40701. Research of EW was partly supported by NSF Grant PHY-0503584.\n\nPublished - euclid.cdm.1223654541.pdf
Submitted - 0612073.pdf
", "abstract": "In the gauge theory approach to the geometric Langlands program, ramification can be described in terms of \"surface operators,\" which are supported on two-dimensional surfaces somewhat as Wilson or 't Hooft operators are supported on curves. We describe the relevant surface operators in N=4 super Yang-Mills theory, and the parameters they depend on, and analyze how S-duality acts on these parameters. Then, after compactifying on a Riemann surface, we show that the hypothesis of S-duality for surface operators leads to a natural extension of the geometric Langlands program for the case of tame ramification. The construction involves an action of the affine Weyl group on the cohomology of the moduli space of Higgs bundles with ramification, and an action of the affine braid group on A-branes or B-branes on this space.", "date": "2008-10-10", "date_type": "published", "publication": "Current Developments in Mathematics", "volume": "2006", "publisher": "International Press", "pagerange": "35-180", "id_number": "CaltechAUTHORS:20160511-095533476", "issn": "1089-6384", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160511-095533476", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" }, { "agency": "NSF", "grant_number": "PHY-0503584" } ] }, "doi": "10.4310/CDM.2006.v2006.n1.a2", "primary_object": { "basename": "0612073.pdf", "url": "https://authors.library.caltech.edu/records/js3z3-npm25/files/0612073.pdf" }, "related_objects": [ { "basename": "euclid.cdm.1223654541.pdf", "url": "https://authors.library.caltech.edu/records/js3z3-npm25/files/euclid.cdm.1223654541.pdf" } ], "resource_type": "article", "pub_year": "2008", "author_list": "Gukov, Sergei and Witten, Edward" }, { "id": "https://authors.library.caltech.edu/records/gwp8z-3y709", "eprint_id": 66685, "eprint_status": "archive", "datestamp": "2023-08-19 21:52:50", "lastmod": "2023-10-18 18:42:08", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gaberdiel-M-R", "name": { "family": "Gaberdiel", "given": "Matthias R." } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Keller-C-A", "name": { "family": "Keller", "given": "Christoph A." }, "orcid": "0000-0003-2592-2012" }, { "id": "Moore-G-W", "name": { "family": "Moore", "given": "Gregory W." } }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" } ] }, "title": "Extremal N = (2, 2) 2D Conformal Field Theories and Constraints of Modularity", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2008 International Press. \n\nReceived June 17, 2008. \n\nWe would like to thank C. Vafa for collaboration at an earlier stage of this project. GM would also like to thank M. Douglas for a past collaboration on closely related issues. We would like to thank F.Denef, T. Gannon, S. Kachru, J. Maldacena, J. Manschot, P. Sarnak, and D. Zagier for useful discussions. \n\nGM and HO thank the organizers of the 37th Paris Summer Institute on Black Holes, Black Rings and Modular Forms, which stimulated progress in this work. SG acknowledges the hospitality of Institut f\u00fcr Theoretische Physik, ETH Zurich, Institute for Advanced Study, Harvard University, Banff Center, the Aspen Center for Physics, the Simons Workshops in 2005, 2006, and 2007, where part of this work was carried out. HO also thanks the Aspen Center for Physics, the Kavli Institute for Theoretical Physics in Santa Barbara, Harvard University, the Simons Workshops in 2005 and 2006 in Stony Brook, the Banff International Research Station, the University of Tokyo, the Galileo Galilei Institute in Florence, the CERN theory institute, and the Ettore Majorana Centre for scientific Culture in Erice, where part of this work was carried out. \n\nThe work of MRG and CAK is supported by the Swiss National Science Foundation. GM is supported by DOE grant DE-FG02-96ER40949. The work of SG and HO is supported in part by DOE grant DE-FG03-92-ER40701. The work of SG is also supported in part by NSF Grant DMS-0635607 and by the Alfred P. Sloan Foundation. The work of HO is also supported in part by NSF grant OISE-0403366, by a Grant-in-Aid for Scientific Research (C) 20540256 from the Japan Society for the Promotion of Science, by the 21st Century COE Visiting Professorship at the University of Tokyo, by the World Premier International Research Center Initiative of MEXT of Japan, and by the Kavli Foundation. Opinions and conclusions expressed here are those of the authors and do not necessarily reflect the views of funding agencies.\n\nPublished - CNTP-2008-0002-0004-a003.pdf
Submitted - 0805.4216.pdf
", "abstract": "We explore the constraints on the spectrum of primary fields implied by modularity of the elliptic genus of N = (2, 2) 2D CFT's. We show that such constraints have nontrivial implications for the existence of \"extremal\" N = (2, 2) conformal field theories. Applications to AdS_3 supergravity and flux compactifications are addressed.", "date": "2008", "date_type": "published", "publication": "Communications in Number Theory and Physics", "volume": "2", "number": "4", "publisher": "International Press", "pagerange": "743-801", "id_number": "CaltechAUTHORS:20160505-104651886", "issn": "1931-4523", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160505-104651886", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Swiss National Science Foundation (SNSF)" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG02-96ER40949" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" }, { "agency": "NSF", "grant_number": "DMS-0635607" }, { "agency": "Alfred P. Sloan Foundation" }, { "agency": "NSF", "grant_number": "OISE-0403366" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "20540256" }, { "agency": "University of Tokyo" }, { "agency": "Ministry of Education, Culture, Sports, Science and Technology (MEXT)" }, { "agency": "Kavli Foundation" } ] }, "other_numbering_system": { "items": [ { "id": "68-2685", "name": "CALT" } ] }, "doi": "10.4310/CNTP.2008.v2.n4.a3", "primary_object": { "basename": "0805.4216.pdf", "url": "https://authors.library.caltech.edu/records/gwp8z-3y709/files/0805.4216.pdf" }, "related_objects": [ { "basename": "CNTP-2008-0002-0004-a003.pdf", "url": "https://authors.library.caltech.edu/records/gwp8z-3y709/files/CNTP-2008-0002-0004-a003.pdf" } ], "resource_type": "article", "pub_year": "2008", "author_list": "Gaberdiel, Matthias R.; Gukov, Sergei; et el." }, { "id": "https://authors.library.caltech.edu/records/eb5rc-are19", "eprint_id": 66986, "eprint_status": "archive", "datestamp": "2023-08-19 19:56:52", "lastmod": "2023-10-18 19:49:40", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Motl-L", "name": { "family": "Motl", "given": "Lubo\u0161" } }, { "id": "Neitzke-A", "name": { "family": "Neitzke", "given": "Andrew" } } ] }, "title": "Equivalence of twistor prescriptions for super Yang-Mills", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2007 International Press. \n\nFirst available in Project Euclid: 24 July 2007. \n\nWe are grateful to Michal Fabinger, Peter Svr\u02c7cek, Cumrun Vafa, Anastasia Volovich, and Edward Witten for very useful discussions. This work was conducted during the period S.G. served as a Clay Mathematics Institute Long-Term Prize Fellow. S.G. is also supported in part by RFBR grant 01-02-17488. The work of L.M. was supported in part by Harvard DOE grant DE-FG01-91ER40654 and the Harvard Society of Fellows. The work of A.N. was supported by NSF grants PHY-0255841 and DMS-0244464.\n\nPublished - Gukov,A.et.al.pdf
Submitted - 0404085.pdf
", "abstract": "There is evidence that one can compute tree-level super Yang-Mills amplitudes using either connected or completely disconnected curves in twistor space. We give a partial explanation of the equivalence between the two computations, by showing that they could both be reduced to the same integral over a moduli space of singular curves, subject to some assumptions about the choices of integration contours. We also formulate a class of new \"intermediate\" prescriptions to calculate the same amplitudes.", "date": "2007-04", "date_type": "published", "publication": "Advances in Theoretical and Mathematical Physics", "volume": "11", "number": "2", "publisher": "International Press", "pagerange": "199-231", "id_number": "CaltechAUTHORS:20160511-104623256", "issn": "1095-0761", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160511-104623256", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Clay Mathematics Institute" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "01-02-17488" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG01-91ER40654" }, { "agency": "Harvard Society of Fellows" }, { "agency": "NSF", "grant_number": "PHY-0255841" }, { "agency": "NSF", "grant_number": "DMS-0244464" } ] }, "doi": "10.4310/ATMP.2007.v11.n2.a1", "primary_object": { "basename": "0404085.pdf", "url": "https://authors.library.caltech.edu/records/eb5rc-are19/files/0404085.pdf" }, "related_objects": [ { "basename": "Gukov,A.et.al.pdf", "url": "https://authors.library.caltech.edu/records/eb5rc-are19/files/Gukov,A.et.al.pdf" } ], "resource_type": "article", "pub_year": "2007", "author_list": "Gukov, Sergei; Motl, Lubo\u0161; et el." }, { "id": "https://authors.library.caltech.edu/records/011h4-5f284", "eprint_id": 3166, "eprint_status": "archive", "datestamp": "2023-08-22 05:21:30", "lastmod": "2023-10-16 15:41:04", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Saraikin-K", "name": { "family": "Saraikin", "given": "Kirill" } }, { "id": "Vafa-C", "name": { "family": "Vafa", "given": "Cumrun" } } ] }, "title": "Entropic principle and asymptotic freedom", "ispublished": "pub", "full_text_status": "public", "keywords": "entropy; black holes; wave functions; string theory", "note": "\u00a9 2006 The American Physical Society. \n\n(Received 20 January 2006; published 21 March 2006) \n\nWe would like to thank R. Dijkgraaf, S. Katz, A. Klemm, M. Ro\u010dek, T. Oliker and H. Ooguri for valuable discussions. We also thank B. Fiol for pointing out a sign error in the large complex structure limit example, that appeared in the first version of the paper. This research was supported in part by NSF Grant Nos. PHY-0244821 and DMS-0244464. K. S. and S. G. are also supported in part by RFBR grant 04-02-16880. We would like to thank the 2005 Simons Workshop on Mathematics and Physics for providing a stimulating environment where part of this work was done. S. G. would also like to thank the KITP at Santa Barbara for hospitality during the completion of this work. While at KITP, the research of S. G. was supported in part by the NSF under grant PHY99-07949.\n\nPublished - GUKprd06.pdf
", "abstract": "Motivated by the recent developments about the Hartle-Hawking wave function associated to black holes, we formulate an entropy functional on the moduli space of Calabi-Yau compactifications. We find that the maximization of the entropy is correlated with the appearance of asymptotic freedom in the effective field theory. The points where the entropy is maximized correspond to points on the moduli which are maximal intersection points of walls of marginal stability for Bogomolnyi-Prasad-Sommerfield states. We also find an intriguing link between extremizing the entropy functional and the points on the moduli space of Calabi-Yau three folds which admit a \"quantum deformed\" complex multiplication.", "date": "2006-03-15", "date_type": "published", "publication": "Physical Review D", "volume": "73", "number": "6", "publisher": "American Physical Society", "pagerange": "Art. No. 066010", "id_number": "CaltechAUTHORS:GUKprd06", "issn": "2470-0010", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:GUKprd06", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-0244821" }, { "agency": "NSF", "grant_number": "DMS-024446" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "04-02-16880" }, { "agency": "NSF", "grant_number": "PHY99-07949" } ] }, "doi": "10.1103/PhysRevD.73.066010", "primary_object": { "basename": "GUKprd06.pdf", "url": "https://authors.library.caltech.edu/records/011h4-5f284/files/GUKprd06.pdf" }, "resource_type": "article", "pub_year": "2006", "author_list": "Gukov, Sergei; Saraikin, Kirill; et el." }, { "id": "https://authors.library.caltech.edu/records/wh2az-ps992", "eprint_id": 66975, "eprint_status": "archive", "datestamp": "2023-08-19 17:31:04", "lastmod": "2023-10-18 19:48:43", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Saraikin-K", "name": { "family": "Saraikin", "given": "Kirill" } }, { "id": "Vafa-C", "name": { "family": "Vafa", "given": "Cumrun" } } ] }, "title": "Stringy wave function for an S^3 cosmology", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2006 The American Physical Society. \n\nReceived 20 January 2006; published 21 March 2006. \n\nWe would like to thank N. Arkani-Hamed, R.Dijkgraaf, A. Neitzke, and H. Ooguri for valuable discussions. This research was supported in part by NSF Grants No. PHY-0244821 and No. DMS-0244464. K. S. and S. G. are also supported in part by RFBR Grant No. 04-02-16880.\n\nPublished - PhysRevD.73.066009.pdf
Submitted - 0505204.pdf
", "abstract": "Using the recent observations of the relation between the Hartle-Hawking wave function and the topological string partition function, we propose a wave function for scalar metric fluctuations on S^3 embedded in a Calabi-Yau manifold. This problem maps to a study of noncritical bosonic string propagating on a circle at the self-dual radius. This can be viewed as a stringy toy model for a quantum cosmology.", "date": "2006-03-15", "date_type": "published", "publication": "Physical Review D", "volume": "73", "number": "6", "publisher": "American Physical Society", "pagerange": "Art. No. 066009", "id_number": "CaltechAUTHORS:20160511-085455539", "issn": "1550-7998", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160511-085455539", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-0244821" }, { "agency": "NSF", "grant_number": "DMS-0244464" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "04-02-16880" } ] }, "doi": "10.1103/PhysRevD.73.066009", "primary_object": { "basename": "0505204.pdf", "url": "https://authors.library.caltech.edu/records/wh2az-ps992/files/0505204.pdf" }, "related_objects": [ { "basename": "PhysRevD.73.066009.pdf", "url": "https://authors.library.caltech.edu/records/wh2az-ps992/files/PhysRevD.73.066009.pdf" } ], "resource_type": "article", "pub_year": "2006", "author_list": "Gukov, Sergei; Saraikin, Kirill; et el." }, { "id": "https://authors.library.caltech.edu/records/v8f4x-j9911", "eprint_id": 66977, "eprint_status": "archive", "datestamp": "2023-08-19 17:06:17", "lastmod": "2023-10-18 19:48:49", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Dunfield-N-M", "name": { "family": "Dunfield", "given": "Nathan M." } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Rasmussen-J", "name": { "family": "Rasmussen", "given": "Jacob" } } ] }, "title": "The Superpolynomial for Knot Homologies", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2006 Taylor & Francis. \n\nWe are grateful to P. Etingof, B. Gornik, V. Kac, M. Khovanov, C. Manolescu, P. Ozsv\u00e1th, A. Schwarz, C. Taubes, C. Vafa, and Z. Szab\u00f3 for valuable discussions. N.D. was partially supported by NSF grant #DMS-0405491 and a Sloan Fellowship. This work was conducted during the period S.G. served as a Clay Mathematics Institute Long-Term Prize Fellow. J.R. was partially supported by an NSF Postdoctoral Fellowship.\n\nSubmitted - 0505662.pdf
", "abstract": "We propose a framework for unifying the sl(N) Khovanov\u2013 Rozansky homology (for all N) with the knot Floer homology. We argue that this unification should be accomplished by a triply graded homology theory that categorifies the HOMFLY polynomial. Moreover, this theory should have an additional formal structure of a family of differentials. Roughly speaking, the triply graded theory by itself captures the large-N behavior of the sl(N) homology, and differentials capture nonstable behavior for small N, including knot Floer homology. The differentials themselves should come from another variant of sl(N) homology, namely the deformations of it studied by Gornik, building on work of Lee.\n\nWhile we do not give a mathematical definition of the triply graded theory, the rich formal structure we propose is powerful enough to make many nontrivial predictions about the existing knot homologies that can then be checked directly. We include many examples in which we can exhibit a likely candidate for the triply graded theory, and these demonstrate the internal consistency of our axioms. We conclude with a detailed study of torus knots, developing a picture that gives new predictions even for the original sl(2) Khovanov homology.", "date": "2006", "date_type": "published", "publication": "Experimental Mathematics", "volume": "15", "number": "2", "publisher": "Taylor & Francis", "pagerange": "129-159", "id_number": "CaltechAUTHORS:20160511-091653426", "issn": "1058-6458", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160511-091653426", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0405491" }, { "agency": "Alfred P. Sloan Foundation" }, { "agency": "Clay Mathematics Institute" }, { "agency": "NSF Postdoctoral Fellowship" } ] }, "doi": "10.1080/10586458.2006.10128956", "primary_object": { "basename": "0505662.pdf", "url": "https://authors.library.caltech.edu/records/v8f4x-j9911/files/0505662.pdf" }, "resource_type": "article", "pub_year": "2006", "author_list": "Dunfield, Nathan M.; Gukov, Sergei; et el." }, { "id": "https://authors.library.caltech.edu/records/80mzw-v9z82", "eprint_id": 66974, "eprint_status": "archive", "datestamp": "2023-08-19 16:27:34", "lastmod": "2023-10-18 19:48:40", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Schwarz-A", "name": { "family": "Schwarz", "given": "Albert" } }, { "id": "Vafa-C", "name": { "family": "Vafa", "given": "Cumrun" } } ] }, "title": "Khovanov-Rozansky Homology and Topological Strings", "ispublished": "pub", "full_text_status": "public", "keywords": "knots, quantum group invariants, knot homology, topological strings, BPS states", "note": "\u00a9 Springer 2005. \n\nReceived: 21 March 2005. \n\nDedicated to the memory of F.A. Berezin. \n\nWe would like to thank D. Bar-Natan, R. Dijkgraaf, M. Gross, K. Intriligator, A. Kapustin, M. Khovanov, A. Klemm, M. Mari\u00f1o, H. Ooguri, J. Roberts and D. Thurston for useful discussions. S.G. would also like to thank the Caltech Particle Theory Group for kind hospitality. The work of A.S. is supported by NSF grant DMS-0204927. This work was conducted during the period S.G. served as a Clay Mathematics Institute Long-Term Prize Fellow. S.G. is also supported in part by RFBR grant 04-02-16880. The work of C.V. is supported in part by NSF grants PHY-0244821 and DMS-0244464.\n\nSubmitted - 0412243.pdf
", "abstract": "We conjecture a relation between the sl(N) knot homology, recently introduced by Khovanov and Rozansky, and the spectrum of BPS states captured by open topological strings. This conjecture leads to new regularities among the sl(N) knot homology groups and suggests that they can be interpreted directly in topological string theory. We use this approach in various examples to predict the sl(N) knot homology groups for all values of N. We verify that our predictions pass some non-trivial checks.", "date": "2005-10", "date_type": "published", "publication": "Letters in Mathematical Physics", "volume": "74", "number": "1", "publisher": "Springer", "pagerange": "53-74", "id_number": "CaltechAUTHORS:20160511-085302183", "issn": "0377-9017", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160511-085302183", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0204927" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "04-02-16880" }, { "agency": "NSF", "grant_number": "PHY-0244821" }, { "agency": "NSF", "grant_number": "DMS-0244464" }, { "agency": "Clay Mathematics Institute" } ] }, "doi": "10.1007/s11005-005-0008-8", "primary_object": { "basename": "0412243.pdf", "url": "https://authors.library.caltech.edu/records/80mzw-v9z82/files/0412243.pdf" }, "resource_type": "article", "pub_year": "2005", "author_list": "Gukov, Sergei; Schwarz, Albert; et el." }, { "id": "https://authors.library.caltech.edu/records/mdwaz-1gg66", "eprint_id": 66978, "eprint_status": "archive", "datestamp": "2023-08-19 16:10:00", "lastmod": "2023-10-18 19:48:52", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Dijkgraaf-R", "name": { "family": "Dijkgraaf", "given": "Robbert" } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Neitzke-A", "name": { "family": "Neitzke", "given": "Andrew" } }, { "id": "Vafa-C", "name": { "family": "Vafa", "given": "Cumrun" } } ] }, "title": "Topological M-theory as Unification of Form Theories of Gravity", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2005 International Press. \n\nFirst available in Project Euclid: 3 April 2006. \n\nWe are grateful to M. Atiyah, J. de Boer, R. Bryant, C. LeBrun, J. Louis, H. Ooguri, M. Ro\u010dek, L. Smolin, C. Taubes, E. Verlinde, and S.-T. Yau for valuable discussions. We would like to thank the 2004 Simons Workshop on Mathematics and Physics and the Aspen Workshop \"Strings, Branes and Superpotentials,\" which led to the development of many of the ideas in this paper. We also thank the organizers of the Strings 2004 conference in Paris for providing a stimulating environment where part of this work was done. S.G. and A.N. would like to thank Caltech Particle Theory Group, where part of this work was done, for kind hospitality. This work was conducted during the period S.G. served as a Clay Mathematics Institute\nLong-Term Prize Fellow. S.G. was also supported in part by RFBR grant 04-02-16880. The research of A.N. and C.V. was supported in part by NSF grants PHY-0244821 and DMS-0244464. The research of R.D. was partly supported by FOM and the NWO Spinoza premium.\n\nPublished - euclid.atmp.1144070454.pdf
Submitted - 0411073.pdf
", "abstract": "We introduce a notion of topological M-theory and argue that it provides a unification of form theories of gravity in various dimensions. Its classical solutions involve G_2 holonomy metrics on 7-manifolds, obtained from a topological action for a 3-form gauge field introduced by Hitchin. We show that by reductions of this 7-dimensional theory, one can classically obtain 6-dimensional topological A and B models, the self-dual sector of loop quantum gravity in four dimensions, and Chern\u2013Simons gravity in 3 dimensions. We also find that the 7-dimensional M-theory perspective sheds some light on the fact that the topological string partition function is a wavefunction, as well as on S-duality between the A and B models. The degrees of freedom of the A and B models appear as conjugate variables in the 7-dimensional theory. Finally, from the topological M-theory perspective, we find hints of an intriguing holographic link between non-supersymmetric Yang\u2013Mills in four dimensions and A model topological strings on twistor space.", "date": "2005-08", "date_type": "published", "publication": "Advances in Theoretical and Mathematical Physics", "volume": "9", "number": "4", "publisher": "International Press", "pagerange": "603-665", "id_number": "CaltechAUTHORS:20160511-091820774", "issn": "1095-0761", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160511-091820774", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Clay Mathematics Institute" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "04-02-16880" }, { "agency": "NSF", "grant_number": "PHY-0244821" }, { "agency": "NSF", "grant_number": "DMS-0244464" }, { "agency": "Stichting voor Fundamenteel Onderzoek der Materie (FOM)" }, { "agency": "Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO)" } ] }, "doi": "10.4310/ATMP.2005.v9.n4.a5", "primary_object": { "basename": "0411073.pdf", "url": "https://authors.library.caltech.edu/records/mdwaz-1gg66/files/0411073.pdf" }, "related_objects": [ { "basename": "euclid.atmp.1144070454.pdf", "url": "https://authors.library.caltech.edu/records/mdwaz-1gg66/files/euclid.atmp.1144070454.pdf" } ], "resource_type": "article", "pub_year": "2005", "author_list": "Dijkgraaf, Robbert; Gukov, Sergei; et el." }, { "id": "https://authors.library.caltech.edu/records/c2y2w-4c831", "eprint_id": 66714, "eprint_status": "archive", "datestamp": "2023-08-19 15:53:43", "lastmod": "2023-10-18 18:44:18", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Martinec-E", "name": { "family": "Martinec", "given": "Emil" } }, { "id": "Moore-G", "name": { "family": "Moore", "given": "Gregory" } }, { "id": "Strominger-A", "name": { "family": "Strominger", "given": "Andrew" } } ] }, "title": "Search for a holographic dual to AdS_3 x S^3 x S^3 x S^1", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2005 International Press.\n\nWe would like to thank J. de Boer, R. Dijkgraaf, J. Maldacena, B. Mazur, H. Ooguri, and K. Skenderis for useful conversations. This work was conducted during the period S.G. served as a Clay Mathematics Institute Long-Term\nPrize Fellow. G.M. thanks the LPTHE theory group at Jussieu, and the KITP at Santa Barbara for hospitality during the course of part of this work. E.M. was supported in part by DOE grant DE-FG02-90ER40560, G.M. by DOE grant DE-FG02-96ER40949, and A.S. by DE-FG02-90ER40654.\n\nPublished - ATMP-2005-0009-0003-a003.pdf
Submitted - 0403090.pdf
", "abstract": "The problem of finding a holographic dual to string theory on AdS_3\u00d7\u00a7^3\u00d7\u00a7^3\u00d7\u00a7^1 is examined in depth. This background supports a large \\CN=4 superconformal symmetry. While in some respects similar to the familiar small \\CN=4 systems on AdS_3\u00d7\u00a7^3\u00d7K^3 and AdS_3\u00d7\u00a7^3\u00d7T^4, there are important qualitative differences. Using an analogue of the elliptic genus for large CN=4 theories we rule out all extant proposals--in their simplest form--for a holographic duality to supergravity at generic values of the background fluxes. Modifications of these extant proposals and other possible duals are discussed.", "date": "2005-06", "date_type": "published", "publication": "Advances in Theoretical and Mathematical Physics", "volume": "9", "number": "3", "publisher": "International Press", "pagerange": "435-525", "id_number": "CaltechAUTHORS:20160506-120757475", "issn": "1095-0761", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160506-120757475", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG02-90ER40560" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG02-96ER40949" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG02-90ER40654" } ] }, "doi": "10.4310/ATMP.2005.v9.n3.a3", "primary_object": { "basename": "0403090.pdf", "url": "https://authors.library.caltech.edu/records/c2y2w-4c831/files/0403090.pdf" }, "related_objects": [ { "basename": "ATMP-2005-0009-0003-a003.pdf", "url": "https://authors.library.caltech.edu/records/c2y2w-4c831/files/ATMP-2005-0009-0003-a003.pdf" } ], "resource_type": "article", "pub_year": "2005", "author_list": "Gukov, Sergei; Martinec, Emil; et el." }, { "id": "https://authors.library.caltech.edu/records/4z911-yts05", "eprint_id": 66723, "eprint_status": "archive", "datestamp": "2023-08-19 15:35:31", "lastmod": "2023-10-18 18:44:53", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" } ] }, "title": "Three-Dimensional Quantum Gravity, Chern-Simons Theory, and the A-Polynomial", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2005 Springer-Verlag. \n\nReceived: 15 July 2003. Accepted: 5 October 2004. Published online: 2 March 2005. \n\nIt is a pleasure to thank D. Bar-Natan, R. Dijkgraaf, N. Dunfield, S. Garoufalidis, R. Gopakumar, G. Horowitz, D. Long, M. Mari\u00f1o, S. Minwalla, H. Ooguri, F. Rodriguez-Villegas, L. Rozansky, C. Vafa, E. Witten, S.-T. Yau, and especially K. Krasnov, G. Moore, A. Strominger, and D. Thurston for valuable and stimulating discussions. This research was conducted during the period S.G. served as a Clay Mathematics Institute Long-Term Prize Fellow. This work is also supported in part by RFBR grant 01-01-00549 and RFBR grant for Young Scientists 02-01-06322. I would also like to thank the University of California at Santa Barbara, Stanford University, California Institute of Technology, and Rutgers University for kind hospitality while this work was in progress. \n\nCommunicated by G.W. Gibbons\n\nSubmitted - 0306165.pdf
", "abstract": "We study three-dimensional Chern-Simons theory with complex gauge group SL(2,\u2102), which has many interesting connections with three-dimensional quantum gravity and geometry of hyperbolic 3-manifolds. We show that, in the presence of a single knotted Wilson loop in an infinite-dimensional representation of the gauge group, the classical and quantum properties of such theory are described by an algebraic curve called the A-polynomial of a knot. Using this approach, we find some new and rather surprising relations between the A-polynomial, the colored Jones polynomial, and other invariants of hyperbolic 3-manifolds. These relations generalize the volume conjecture and the Melvin-Morton-Rozansky conjecture, and suggest an intriguing connection between the SL(2,\u2102) partition function and the colored Jones polynomial.", "date": "2005-04", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "255", "number": "3", "publisher": "Springer", "pagerange": "577-627", "id_number": "CaltechAUTHORS:20160509-071118060", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160509-071118060", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Russian Foundation for Basic Research", "grant_number": "01-01-00549" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "02-01-06322" }, { "agency": "Clay Mathematics Institute" } ] }, "doi": "10.1007/s00220-005-1312-y", "primary_object": { "basename": "0306165.pdf", "url": "https://authors.library.caltech.edu/records/4z911-yts05/files/0306165.pdf" }, "resource_type": "article", "pub_year": "2005", "author_list": "Gukov, Sergei" }, { "id": "https://authors.library.caltech.edu/records/p9dxd-0p698", "eprint_id": 3167, "eprint_status": "archive", "datestamp": "2023-08-22 01:49:38", "lastmod": "2023-10-16 15:41:07", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Kachru-S", "name": { "family": "Kachru", "given": "Shamit" } }, { "id": "Liu-Xiao", "name": { "family": "Liu", "given": "Xiao" } }, { "id": "McAllister-L", "name": { "family": "McAllister", "given": "Liam" } } ] }, "title": "Heterotic moduli stabilization with fractional Chern-Simons invariants", "ispublished": "pub", "full_text_status": "public", "keywords": "superstrings; membrane theory; grand unified theory; Chern-Simons theory; spontaneous symmetry breaking", "note": "\u00a92004 The American Physical Society \n\n(Received 11 November 2003; published 29 April 2004) \n\nWe would like to thank B. Acharya, N. Arkani-Hamed, P. Aspinwall, M. Becker, K. Dasgupta, M. Dine, M. Douglas, R. Kallosh, A. Krause, E. Silverstein, S. Thomas, S. Trivedi, and E. Witten for interesting discussions on related subjects. S.G. is supported in part by the RFBR Grant No. 01-01-00549 and the RFBR grant for Young Scientists 02-01-06322. The work of S.K. is supported in part by the David and Lucile Packard Foundation, National Science Foundation Grant No. PHY-0097915, and the DOE under Contract No. DE-AC03-76SF00515. The work of L.M. is supported by the National Science Foundation.\n\nPublished - GUKprd04.pdf
", "abstract": "We show that fractional flux from Wilson lines can stabilize the moduli of heterotic string compactifications on Calabi-Yau threefolds. We observe that the Wilson lines used in GUT symmetry breaking naturally induce a fractional flux. When combined with a hidden-sector gaugino condensate, this generates a potential for the complex structure moduli, K\u00e4hler moduli, and dilaton. This potential has a supersymmetric AdS minimum at moderately weak coupling and large volume. Notably, the necessary ingredients for this construction are often present in realistic models. We explore the type IIA dual phenomenon, which involves Wilson lines in D6-branes wrapping a three-cycle in a Calabi-Yau threefold, and comment on the nature of the fractional instantons that change the Chern-Simons invariant.", "date": "2004-04-15", "date_type": "published", "publication": "Physical Review D", "volume": "69", "number": "8", "publisher": "American Physical Society", "pagerange": "Art. No. 086008", "id_number": "CaltechAUTHORS:GUKprd04", "issn": "2470-0010", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:GUKprd04", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Russian Foundation for Basic Research", "grant_number": "01-01-00549" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "02-01-06322" }, { "agency": "David and Lucile Packard Foundation" }, { "agency": "NSF", "grant_number": "PHY-0097915" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-AC03-76SF00515" } ] }, "doi": "10.1103/PhysRevD.69.086008", "primary_object": { "basename": "GUKprd04.pdf", "url": "https://authors.library.caltech.edu/records/p9dxd-0p698/files/GUKprd04.pdf" }, "resource_type": "article", "pub_year": "2004", "author_list": "Gukov, Sergei; Kachru, Shamit; et el." }, { "id": "https://authors.library.caltech.edu/records/2ha7d-ah715", "eprint_id": 2018, "eprint_status": "archive", "datestamp": "2023-08-22 01:35:09", "lastmod": "2023-10-13 23:09:13", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Takanayagi-Tadashi", "name": { "family": "Takayanagi", "given": "Tadashi" } }, { "id": "Toumbas-N", "name": { "family": "Toumbas", "given": "Nicolaos" } } ] }, "title": "Flux backgrounds in 2D string theory", "ispublished": "pub", "full_text_status": "public", "keywords": "Superstrings and Heterotic Strings, D-branes, Black Holes in String Theory, Matrix Models", "note": "\u00a9 Institute of Physics 2004 \n\nReceived 20 January 2004, accepted for publication 4 March 2004, Published 19 March 2004 \n\nWe would like to thank V. Balasubramanian, J. de Boer, R. Dijkgraaf, T. Eguchi, J. Gomis, P.M. Ho, A. Kapustin, J. Karczmarek, Y. Matsuo, J. Mcgreevy, S. Murthy, S. Terashima, C. Vafa, H. Verlinde, X. Yi and especially I. Klebanov, J. Maldacena, S. Minwalla, N. Seiberg and A. Strominger for valuable discussions. This work was conducted during the period S.G. served as a Clay Mathematics Institute Long-Term Prize Fellow. S.G. is also supported in part by RFBR grant 01-02-17488. T.T. would like to thank Institute for Advanced Study for its hospitality. The work of T.T. was supported in part by DOE grant DE-FG03-91ER40654. \n\nE-print number: hep-th/0312208\n\nPublished - GUKjhep04.pdf
", "abstract": "We study RR flux backgrounds in two dimensional type 0 string theories. In particular, we study the relation between the 0A matrix model and the extremal black hole in two dimensions. Using T-duality we find a dual flux background in type 0B theory and propose its matrix model description. When the Fermi level \u03bc is set to zero this system remains weakly coupled and exhibits a larger symmetry related to the structure of flux vacua. Finally, we construct a two dimensional type-IIB background as an orbifold of the 0B background.", "date": "2004-03", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2004", "number": "3", "publisher": "Springer", "pagerange": "Art. No. 017", "id_number": "CaltechAUTHORS:GUKjhep04", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:GUKjhep04", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Clay Mathematics Institute" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "01-02-17488" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-91ER40654" } ] }, "doi": "10.1088/1126-6708/2004/03/017", "primary_object": { "basename": "GUKjhep04.pdf", "url": "https://authors.library.caltech.edu/records/2ha7d-ah715/files/GUKjhep04.pdf" }, "resource_type": "article", "pub_year": "2004", "author_list": "Gukov, Sergei; Takayanagi, Tadashi; et el." }, { "id": "https://authors.library.caltech.edu/records/4bgvm-3at53", "eprint_id": 66990, "eprint_status": "archive", "datestamp": "2023-08-19 13:11:22", "lastmod": "2023-10-18 19:50:00", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Acharya-B-S", "name": { "family": "Acharya", "given": "Bobby S." } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" } ] }, "title": "M theory and singularities of exceptional holonomy manifolds", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2003 Elsevier B.V. \n\nAccepted 28 October 2003. editor: A. Schwimmer. \n\nVarious topics covered in this review are based on the work done together with A. Brandhuber, J. Gomis, S. Gubser, X. de la Ossa, D. Tong, J. Sparks, C. Vafa, E. Witten, S.-T. Yau, and E. Zaslow, whom we wish to thank for many useful discussions and collaboration. This work was conducted during the period S.G. served as a Clay Mathematics Institute Long-Term Prize Fellow. The work of S.G. is also supported in part by RFBR grant 01-01-00549 and RFBR grant for Young Scientists 02-01-06322.\n\nSubmitted - 0409191.pdf
", "abstract": "M theory compactifications on G_2 holonomy manifolds, whilst supersymmetric, require singularities in order to obtain non-Abelian gauge groups, chiral fermions and other properties necessary for a realistic model of particle physics. We review recent progress in understanding the physics of such singularities. Our main aim is to describe the techniques which have been used to develop our understanding of M theory physics near these singularities. In parallel, we also describe similar sorts of singularities in Spin(7) holonomy manifolds which correspond to the properties of three dimensional field theories. As an application, we review how various aspects of strongly coupled gauge theories, such as confinement, mass gap and non-perturbative phase transitions may be given a simple explanation in M theory.", "date": "2004-03", "date_type": "published", "publication": "Physics Reports", "volume": "392", "number": "3", "publisher": "Elsevier", "pagerange": "121-189", "id_number": "CaltechAUTHORS:20160511-110724676", "issn": "0370-1573", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160511-110724676", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Clay Mathematics Institute" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "01-01-00549" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "02-01-06322" } ] }, "doi": "10.1016/j.physrep.2003.10.017", "primary_object": { "basename": "0409191.pdf", "url": "https://authors.library.caltech.edu/records/4bgvm-3at53/files/0409191.pdf" }, "resource_type": "article", "pub_year": "2004", "author_list": "Acharya, Bobby S. and Gukov, Sergei" }, { "id": "https://authors.library.caltech.edu/records/v7gfx-sd755", "eprint_id": 66710, "eprint_status": "archive", "datestamp": "2023-08-19 13:11:14", "lastmod": "2023-10-18 18:44:02", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Vafa-C", "name": { "family": "Vafa", "given": "Cumrun" } } ] }, "title": "Rational Conformal Field Theories and Complex Multiplication", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2004 Springer-Verlag. \n\nReceived: 18 July 2003. Accepted: 26 August 2003. Published online: 23 January 2004.\n\nWe would like to thank D. Kazhdan and B. Mazur for many illuminating discussions on complex multiplication. We are also grateful to J. de Jong, J. Maldacena, K. Oguiso, H. Ooguri, F. Oort, A. Recknagel, S. Shenker, F. Rodriguez-Villegas, and E. Witten for valuable discussions. This research was partially conducted during the period S.G. served as a Clay Mathematics Institute Long-Term Prize\nFellow. The work of S.G. is also supported in part by grant RFBR No. 01-02-17488, and the Russian President's grant No. 00-15-99296. The work of C.V. is supported in part by NSF grants PHY-9802709 and DMS 0074329. \n\nCommunicated by Y. Kawahigashi.\n\nSubmitted - 0203213.pdf
", "abstract": "We study the geometric interpretation of two dimensional rational conformal field theories, corresponding to sigma models on Calabi-Yau manifolds. We perform a detailed study of RCFT's corresponding to the T ^2 target and identify the Cardy branes with geometric branes. The T ^2 's leading to RCFT's admit \"complex multiplication\" which characterizes Cardy branes as specific D0-branes. We propose a condition for the conformal sigma model to be RCFT for arbitrary Calabi-Yau n-folds, which agrees with the known cases. Together with recent conjectures by mathematicians it appears that rational conformal theories are not dense in the space of all conformal theories, and sometimes appear to be finite in number for Calabi-Yau n-folds for n>2. RCFT's on K3 may be dense. We speculate about the meaning of these special points in the moduli spaces of Calabi-Yau n-folds in connection with freezing geometric moduli.", "date": "2004-03", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "246", "number": "1", "publisher": "Springer", "pagerange": "181-210", "id_number": "CaltechAUTHORS:20160506-080721343", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160506-080721343", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Russian Foundation for Basic Research", "grant_number": "01-02-17488" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "00-15-99296" }, { "agency": "NSF", "grant_number": "PHY-9802709" }, { "agency": "NSF", "grant_number": "DMS-0074329" }, { "agency": "Clay Mathematics Institute" } ] }, "doi": "10.1007/s00220-003-1032-0", "primary_object": { "basename": "0203213.pdf", "url": "https://authors.library.caltech.edu/records/v7gfx-sd755/files/0203213.pdf" }, "resource_type": "article", "pub_year": "2004", "author_list": "Gukov, Sergei and Vafa, Cumrun" }, { "id": "https://authors.library.caltech.edu/records/kr7zj-3pg39", "eprint_id": 3766, "eprint_status": "archive", "datestamp": "2023-08-22 00:49:29", "lastmod": "2023-10-16 16:09:06", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Dijkgraaf-R", "name": { "family": "Dijkgraaf", "given": "Robbert" } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Kazakov-V-A", "name": { "family": "Kazakov", "given": "Vladimir A." } }, { "id": "Vafa-C", "name": { "family": "Vafa", "given": "Cumrun" } } ] }, "title": "Perturbative analysis of gauged matrix models", "ispublished": "pub", "full_text_status": "public", "keywords": "M-theory; gauge field theory; spontaneous symmetry breaking; perturbation theory", "note": "\u00a92003 The American Physical Society. \n\nReceived 5 May 2003; published 18 August 2003. \n\nWe would like to thank M. Aganagic, R. Bousso, F. Cachazo, S. J. Gates, Jr., M. Marino, A. Marshakov, H. Ooguri, S. Theisen, and K. Zarembo for valuable discussions. The research of R.D. is partly supported by FOM and the CMPA grant of the University of Amsterdam. S.G. is supported by the Clay Mathematics Institute, RFBR grants 01-01-00549 and 02-01-06322. V.A.K. is partly supported by European Union under the RTN contracts HPRN-CT-2000-00122 and -00131. C.V. is partly supported by NSF grants PHY-9802709 and DMS-0074329. We would like to thank the Max Planck Institute in Potsdam (V.A.K.), Ecole Normale Superieure (S.G.), and Harvard University (R.D.) for kind hospitality during part of this work.\n\nPublished - DIJprd03.pdf
", "abstract": "We analyze perturbative aspects of gauged matrix models, including those where classically the gauge symmetry is partially broken. Ghost fields play a crucial role in the Feynman rules for these vacua. We use this formalism to elucidate the fact that nonperturbative aspects of [script N] = 1 gauge theories can be computed systematically using perturbative techniques of matrix models, even if we do not possess an exact solution for the matrix model. As examples we show how the Seiberg-Witten solution for [script N] = 2 gauge theory, the Montonen-Olive modular invariance for [script N] = 1*, and the superpotential for the Leigh-Strassler deformation of [script N] = 4 can be systematically computed in perturbation theory of the matrix model or gauge theory (even though in some of these cases an exact answer can also be obtained by summing up planar diagrams of matrix models).", "date": "2003-08-15", "date_type": "published", "publication": "Physical Review D", "volume": "68", "number": "4", "publisher": "American Physical Society", "pagerange": "Art. No. 045007", "id_number": "CaltechAUTHORS:DIJprd03", "issn": "2470-0010", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:DIJprd03", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Stichting voor Fundamenteel Onderzoek der Materie (FOM)" }, { "agency": "University of Amsterdam" }, { "agency": "Clay Mathematics Institute" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "01-01-00549" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "02-01-06322" }, { "agency": "European Union", "grant_number": "HPRN-CT-2000-00122" }, { "agency": "European Union", "grant_number": "HPRN-CT-2000-00131" }, { "agency": "NSF", "grant_number": "PHY-9802709" }, { "agency": "NSF", "grant_number": "DMS-0074329" } ] }, "doi": "10.1103/PhysRevD.68.045007", "primary_object": { "basename": "DIJprd03.pdf", "url": "https://authors.library.caltech.edu/records/kr7zj-3pg39/files/DIJprd03.pdf" }, "resource_type": "article", "pub_year": "2003", "author_list": "Dijkgraaf, Robbert; Gukov, Sergei; et el." }, { "id": "https://authors.library.caltech.edu/records/hj1j4-bk116", "eprint_id": 2015, "eprint_status": "archive", "datestamp": "2023-08-22 00:14:57", "lastmod": "2023-10-13 23:09:07", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Sparks-J", "name": { "family": "Sparks", "given": "James" } }, { "id": "Tong-David", "name": { "family": "Tong", "given": "David" } } ] }, "title": "Conifold transitions and five-brane condensation in M-theory on Spin(7) manifolds", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 Institute of Physics 2003 \n\nReceived 23 September 2002, in final form 6 January 2003, Published 28 January 2003, Print publication: Issue 4 (21 February 2003) \n\nWe wish to thank Roman Jackiw, Neil Lambert, Igor Polyubin, Ashoke Sen, Andrew Strominger, Jan Troost, Cumrun Vafa,Ashvin Vishwanath, Eric Zaslow and especially Bobby Acharya and Edward Witten for useful discussions. SG and DT would also like to thank the Isaac Newton Institute for Mathematical Sciences, Cambridge, UK, and SG would further like to thank the New High Energy Theory Center at Rutgers University for kind hospitality during the course of this work. This research was conducted during the period SG served as a Clay Mathematics Institute Long-Term Prize Fellow. The work of SG is also supported in part by grant RFBR no 01-02-17488, and the Russian President's grant no 00-15-99296. DT is a Pappalardo fellow and is grateful to the Pappalardo family for their kind support. The work of DT is also supported in part by funds provided by the US Department of Energy (DOE) under cooperative research agreement no DF-FC02-94ER40818.\n\nPublished - GUKcqg03.pdf
Submitted - 0207244v2.pdf
", "abstract": "We conjecture a topology-changing transition in M-theory on a non-compact asymptotically conical Spin(7) manifold, where a 5-sphere collapses and a Bbb CP2 bolt grows. We argue that the transition may be understood as the condensation of M5-branes wrapping S5. Upon reduction to ten dimensions, it has a physical interpretation as a transition of D6-branes lying on calibrated submanifolds of flat space. In yet another guise, it may be seen as a geometric transition between two phases of type IIA string theory on a G2 holonomy manifold with either wrapped D6-branes, or background Ramond\u2013Ramond flux. This is the first non-trivial example of a topology-changing transition with only 1/16 supersymmetry.", "date": "2003-02-21", "date_type": "published", "publication": "Classical and Quantum Gravity", "volume": "20", "number": "4", "publisher": "IOP", "pagerange": "665-705", "id_number": "CaltechAUTHORS:GUKcqg03", "issn": "0264-9381", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:GUKcqg03", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Clay Mathematics Institute" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "01-02-17488" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "00-15-99296" }, { "agency": "Pappalardo Fellowship" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FC02-94ER40818" } ] }, "doi": "10.1088/0264-9381/20/4/306", "primary_object": { "basename": "0207244v2.pdf", "url": "https://authors.library.caltech.edu/records/hj1j4-bk116/files/0207244v2.pdf" }, "related_objects": [ { "basename": "GUKcqg03.pdf", "url": "https://authors.library.caltech.edu/records/hj1j4-bk116/files/GUKcqg03.pdf" } ], "resource_type": "article", "pub_year": "2003", "author_list": "Gukov, Sergei; Sparks, James; et el." }, { "id": "https://authors.library.caltech.edu/records/2xk03-s5993", "eprint_id": 66715, "eprint_status": "archive", "datestamp": "2023-08-19 10:37:16", "lastmod": "2023-10-18 18:44:24", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Yau-Shing-Tung", "name": { "family": "Yau", "given": "Shing-Tung" } }, { "id": "Zaslow-E", "name": { "family": "Zaslow", "given": "Eric" } } ] }, "title": "Duality and Fibrations on G_2 Manifolds", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2003 T\u00fcrkiye Bilimsel ve Teknolojik Ara\u015ft\u0131rma Kurumu (T\u00dcB\u0130TAK). \n\nWe would like to thank A. Strominger, R. Thomas, C. Vafa, and E. Witten for instructive discussions. This research was conducted during the period S.G. served as a Clay\nMathematics Institute Long-Term Prize Fellow. The work of S.G. is also supported in part by grant RFBR No. 01-02-17488, and the Russian President's grant No. 00-15-99296. The work of S.T.Y. is supported in part by grants DMS-0074329 and DMS-9803347. The work of E.Z. is supported in part by NSF grant DMS-0072504 and by an Alfred P. Sloan Foundation Fellowship.\n\nSubmitted - 0203217.pdf
", "abstract": "We argue that G_2 manifolds for M-theory admitting string theory Calabi-Yau duals are fibered by coassociative submanifolds. Dual theories are constructed using the moduli space of M-five-brane fibers as target space. Mirror symmetry and various string and M-theory dualities involving G_2 manifolds may be incorporated into this framework. To give some examples, we construct two non-compact manifolds with G_2 structures: one with a K3 fibration, and one with a torus fibration and a metric of G_2 holonomy. Kaluza-Klein reduction of the latter solution gives abelian BPS monopoles in 3 + 1 dimensions.", "date": "2003", "date_type": "published", "publication": "Turkish Journal of Mathematics", "volume": "27", "number": "1", "publisher": "Scientific and Technical Research Council of Turkey", "pagerange": "61-97", "id_number": "CaltechAUTHORS:20160506-122921323", "issn": "1303-6149", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160506-122921323", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Russian Foundation for Basic Research", "grant_number": "01-02-17488" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "00-15-99296" }, { "agency": "NSF", "grant_number": "DMS-0074329" }, { "agency": "NSF", "grant_number": "DMS-9803347" }, { "agency": "NSF", "grant_number": "DMS-0072504" }, { "agency": "Alfred P. Sloan Foundation Fellowship" } ] }, "doi": "10.48550/arXiv.0203217v1", "primary_object": { "basename": "0203217.pdf", "url": "https://authors.library.caltech.edu/records/2xk03-s5993/files/0203217.pdf" }, "resource_type": "article", "pub_year": "2003", "author_list": "Gukov, Sergei; Yau, Shing-Tung; et el." }, { "id": "https://authors.library.caltech.edu/records/trfyf-k1r59", "eprint_id": 66691, "eprint_status": "archive", "datestamp": "2023-08-19 10:10:05", "lastmod": "2023-10-18 18:42:33", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Tong-David", "name": { "family": "Tong", "given": "David" } } ] }, "title": "D-brane probes of G_2 holonomy manifolds", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2002 The American Physical Society. \n\nReceived 5 March 2002; published 3 October 2002. \n\nWe are grateful to B. Acharya, M. Aganagic, N. Constable, A. Hanany, J. Sparks, N. Seiberg, M. Strassler, C. Vafa and E. Witten for useful discussions. The work of S.G. is also supported in part by grant RFBR No. 01-02-17488, and the Russian President's grant No. 00-15-99296. D.T. is supported in part by funds provided by the U.S. Department of Energy (DOE) under cooperative research agreement No. DF-FC02-94ER40818.\n\nPublished - PhysRevD.66.087901.pdf
Submitted - 0202125.pdf
", "abstract": "We describe how mirror symmetry of three-dimensional N=1 supersymmetric gauge theories can be used to determine the theory on the world volume of a D2-brane probe of manifolds with G_2 holonomy.", "date": "2002-10-15", "date_type": "published", "publication": "Physical Review D", "volume": "66", "number": "8", "publisher": "American Physical Society", "pagerange": "Art. No. 087901", "id_number": "CaltechAUTHORS:20160505-113949597", "issn": "2470-0010", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160505-113949597", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Russian Foundation for Basic Research", "grant_number": "01-02-17488" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "00-15-99296" }, { "agency": "Department of Energy (DOE)", "grant_number": "DF-FC02-94ER40818" } ] }, "doi": "10.1103/PhysRevD.66.087901", "primary_object": { "basename": "0202125.pdf", "url": "https://authors.library.caltech.edu/records/trfyf-k1r59/files/0202125.pdf" }, "related_objects": [ { "basename": "PhysRevD.66.087901.pdf", "url": "https://authors.library.caltech.edu/records/trfyf-k1r59/files/PhysRevD.66.087901.pdf" } ], "resource_type": "article", "pub_year": "2002", "author_list": "Gukov, Sergei and Tong, David" }, { "id": "https://authors.library.caltech.edu/records/n5yd3-kpp95", "eprint_id": 66675, "eprint_status": "archive", "datestamp": "2023-08-19 10:02:26", "lastmod": "2023-10-18 18:41:33", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Haack-M", "name": { "family": "Haack", "given": "Michael" } } ] }, "title": "IIA string theory on Calabi-Yau fourfolds with background fluxes", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2002 Elsevier Science B.V.\n\nReceived 24 April 2002, Accepted 30 May 2002, Available online 17 June 2002.\n\nWe thank M. Berg, R. Kallosh, J. Louis, A. Strominger, and E. Witten for useful discussions. This research was partially conducted during the period S.G. served as a Clay Mathematics Institute Long-Term Prize Fellow. The work of S.G. is also supported in part by grant RFBR No. 01-02-17488, and the Russian President's grant No. 00-15-99296. M.H. would like to thank the University of Princeton and especially I. Klebanov for hospitality at the beginning of the work. Moreover M.H. thanks the DFG for financial support and his work was supported in part by INFN, by the EC contract HPRN-CT-2000-00122, by the EC contract HPRN-CT-2000-00148, by the INTAS contract 99-0-590 and by the MURST-COFIN contract 2001-025492.\n\nSubmitted - 0203267.pdf
", "abstract": "Looking for string vacua with fixed moduli, we study compactifications of type IIA string theory on Calabi\u2013Yau fourfolds in the presence of generic Ramond\u2013Ramond fields. We explicitly derive the (super)potential induced by Ramond\u2013Ramond fluxes performing a Kaluza\u2013Klein reduction of the ten-dimensional effective action. This can be conveniently achieved in a formulation of the massive type IIA supergravity where all Ramond\u2013Ramond fields appear in a democratic way. The result agrees with the general formula for the superpotential written in terms of calibrations. We further notice that for generic Ramond\u2013Ramond fluxes all geometric moduli are stabilized and one finds non-supersymmetric vacua at positive values of the scalar potential.", "date": "2002-09-09", "date_type": "published", "publication": "Nuclear Physics B", "volume": "639", "number": "1-2", "publisher": "Elsevier", "pagerange": "95-128", "id_number": "CaltechAUTHORS:20160505-083954824", "issn": "0550-3213", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160505-083954824", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Clay Mathematics Institute" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "01-02-17488" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "00-15-99296" }, { "agency": "Deutsche Forschungsgemeinschaft (DFG)" }, { "agency": "Istituto Nazionale di Fisica Nucleare (INFN)" }, { "agency": "European Union", "grant_number": "HPRN-CT-2000-00122" }, { "agency": "European Union", "grant_number": "HPRN-CT-2000-00148" }, { "agency": "INTAS", "grant_number": "99-0-590" }, { "agency": "Ministero dell 'Universit\u00e0 e della Ricerca Scientifica e Tecnologica (MURST)", "grant_number": "2001-025492" } ] }, "doi": "10.1016/S0550-3213(02)00442-X", "primary_object": { "basename": "0203267.pdf", "url": "https://authors.library.caltech.edu/records/n5yd3-kpp95/files/0203267.pdf" }, "resource_type": "article", "pub_year": "2002", "author_list": "Gukov, Sergei and Haack, Michael" }, { "id": "https://authors.library.caltech.edu/records/9t108-2x680", "eprint_id": 2017, "eprint_status": "archive", "datestamp": "2023-08-21 23:38:59", "lastmod": "2023-10-13 23:09:11", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Acharya-B-S", "name": { "family": "Acharya", "given": "Bobby S." } }, { "id": "De-La-Ossa-X", "name": { "family": "De La Ossa", "given": "Xenia" } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" } ] }, "title": "G-flux, supersymmetry and Spin(7) manifolds", "ispublished": "pub", "full_text_status": "public", "keywords": "M-Theory, Superstring vacua", "note": "\u00a9 Institute of Physics 2002 \n\nReceived 25 July 2002, accepted for publication 20 September 2002, Published 4 November 2002\n\nWe would like to thank P. Candelas, D. Joyce, J. Sparks, and E. Witten for useful discussions. This research was partially conducted during the period S.G. served as a Clay Mathematics Institute Long-Term Prize Fellow. The work of S.G. is also supported in part by grant RFBR No. 01-02-17488, and the Russian President's grant No. 00-15-99296.\n\nE-print number: hep-th/0201227\n\nPublished - ACHjhep02.pdf
", "abstract": "In this note we study warped compactifications of M-theory on manifolds of Spin(7) holonomy in the presence of background 4-form flux. The explicit expression for the superpotential can be given in terms of the self-dual Cayley calibration on the Spin(7) manifold, in agreement with the general formula proposed in hep-th/9911011.", "date": "2002-09", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2002", "number": "9", "publisher": "Springer", "pagerange": "Art. No. 047", "id_number": "CaltechAUTHORS:ACHjhep02", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:ACHjhep02", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Clay Mathematics Institute" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "01-02-17488" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "00-15-99296" } ] }, "doi": "10.1088/1126-6708/2002/09/047", "primary_object": { "basename": "ACHjhep02.pdf", "url": "https://authors.library.caltech.edu/records/9t108-2x680/files/ACHjhep02.pdf" }, "resource_type": "article", "pub_year": "2002", "author_list": "Acharya, Bobby S.; De La Ossa, Xenia; et el." }, { "id": "https://authors.library.caltech.edu/records/y6bfe-6cy93", "eprint_id": 66688, "eprint_status": "archive", "datestamp": "2023-08-19 09:16:46", "lastmod": "2023-10-18 18:42:18", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Tong-David", "name": { "family": "Tong", "given": "David" } } ] }, "title": "D-Brane probes of Special Holonomy Manifolds, and Dynamics of N=1 Three-Dimensional Gauge Theories", "ispublished": "pub", "full_text_status": "public", "keywords": "Field Theories in Lower Dimensions, Duality in Gauge Field Theories,\nBrane Dynamics in Gauge Theories", "note": "\u00a9 2002 SISSA/ISAS. \n\nReceived: March 20, 2002; Accepted: April 26, 2002. \n\nWe are grateful to B. Acharya, M. Aganagic, N. Constable, A. Hanany, J. Sparks, N. Seiberg, M. Strassler, C. Vafa and E. Witten for useful discussions. This research was conducted during the period S.G. served as a Clay Mathematics Institute Long-Term Prize Fellow. The work of S.G. is also supported in part by grant RFBR No. 01-02-17488, and the Russian President's grant No. 00-15-99296. D.T. is a Pappalardo fellow and would like to thank the Pappalardo family for their largesse. The work of D.T. also supported in part by funds provided by the U.S. Department of Energy (D.O.E.) under cooperative research agreement #DF-FC02-94ER40818.\n\nSubmitted - 0202126.pdf
", "abstract": "Using D2-brane probes, we study various properties of M-theory on singular, non-compact manifolds of G_2 and Spin(7) holonomy. We derive mirror pairs of N = 1 supersymmetric three-dimensional gauge theories, and apply this technique to realize exceptional holonomy manifolds as both Coulomb and Higgs branches of the D2-brane world-volume theory. We derive a \"G_2 quotient construction'' of non-compact manifolds which admit a metric of G_2 holonomy. We further discuss the moduli space of such manifolds, including the structure of geometrical transitions in each case. For completeness, we also include familiar examples of manifolds withSU(3) and Sp(2) holonomy, where some of the new ideas are clarified and tested.", "date": "2002-04", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2002", "number": "4", "publisher": "Springer", "pagerange": "Art. No. 50", "id_number": "CaltechAUTHORS:20160505-110509143", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160505-110509143", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Russian Foundation for Basic Research", "grant_number": "01-02-17488" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "00-15-99296" }, { "agency": "Pappalardo Fellowship" }, { "agency": "Department of Energy (DOE)", "grant_number": "DF-FC02-94ER40818" }, { "agency": "Clay Mathematics Institute" } ] }, "doi": "10.1088/1126-6708/2002/04/050", "primary_object": { "basename": "0202126.pdf", "url": "https://authors.library.caltech.edu/records/y6bfe-6cy93/files/0202126.pdf" }, "resource_type": "article", "pub_year": "2002", "author_list": "Gukov, Sergei and Tong, David" }, { "id": "https://authors.library.caltech.edu/records/jn6bs-kmc05", "eprint_id": 66712, "eprint_status": "archive", "datestamp": "2023-08-19 09:13:33", "lastmod": "2023-10-18 18:44:15", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Sparks-J", "name": { "family": "Sparks", "given": "James" } } ] }, "title": "M-theory on Spin(7) manifolds", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2002 Elsevier B.V. \n\nReceived 19 November 2001, Accepted 9 January 2002. \n\nWe wish to thank K. Costello, G. Gibbons, C. Herzog, J. Maldacena, N. Nekrasov, C. N\u00fa\u00f1ez, C. Pope, E. Rabinovici, S. Schafer-Nameki, A. Strominger, C. Vafa, and E. Witten for useful discussions. This research was partially conducted during the period S.G. served as a Clay Mathematics Institute Long-Term Prize Fellow. The work of S.G. is also supported in part by grant RFBR No. 01-02-17488, and the Russian President's grant No. 00-15-99296.\n\nSubmitted - 0109025.pdf
", "abstract": "We study M-theory on two classes of manifolds of Spin(7) holonomy that are developing an isolated conical singularity. We construct explicitly a new class of Spin(7) manifolds and analyse in detail the topology of the corresponding classical spacetimes. We discover also an intricate interplay between various anomalies in M-theory, string theory, and gauge theory within these models, and in particular find a connection between half-integral G-fluxes in M-theory and Chern\u2013Simons terms of the N=1, D=3 effective theory.", "date": "2002-03-18", "date_type": "published", "publication": "Nuclear Physics B", "volume": "625", "number": "1-2", "publisher": "Elsevier", "pagerange": "3-69", "id_number": "CaltechAUTHORS:20160506-084420068", "issn": "0550-3213", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160506-084420068", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Russian Foundation for Basic Research", "grant_number": "01-02-17488" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "00-15-99296" } ] }, "doi": "10.1016/S0550-3213(02)00018-4", "primary_object": { "basename": "0109025.pdf", "url": "https://authors.library.caltech.edu/records/jn6bs-kmc05/files/0109025.pdf" }, "resource_type": "article", "pub_year": "2002", "author_list": "Gukov, Sergei and Sparks, James" }, { "id": "https://authors.library.caltech.edu/records/a7jkf-bgb64", "eprint_id": 66709, "eprint_status": "archive", "datestamp": "2023-08-19 08:26:47", "lastmod": "2023-10-18 18:43:55", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Berkovits-N", "name": { "family": "Berkovits", "given": "Nathan" } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Vallilo-B-C", "name": { "family": "Vallilo", "given": "Brenno Carlini" } } ] }, "title": "Superstrings in 2D backgrounds with R\u2013R flux and new extremal black holes", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2001 Elsevier B.V. \n\nReceived 7 August 2001, Accepted 15 August 2001, Available online 5 October 2001. \n\nWe are grateful to C.G. Callan, O. Chand\u0131\u0301a, A.T. Filippov, G.T. Horowitz, J. Maldacena, D. Nedel, R. Plesser, H. Ooguri, V. Rivelles, J.H. Schwarz, N. Seiberg, S. Shenker, A. Strominger, C. Vafa, and E. Witten for useful discussions and comments. The work of N.B. is supported in part by CNPq grant 300256/94-9, Pronex 66.2002/1998-9, and FAPESP grant 99/12763-0. This research was partially conducted during the period N.B. served as a Clay Mathematics Institute Prize Fellow and S.G. served as a Clay Mathematics Institute Long-Term Prize Fellow. The work of S.G. is also supported in part by the Caltech Discovery Fund, NSF grant No. PHY99-07949, grant RFBR No. 01-02-17488, and the Russian President's grant No. 00-15-99296. The work of B.C.V. is supported by FAPESP grant No 00/02230-3. N.B. and S.G. are grateful to the California Institute of Technology, where part of this work was done, for hospitality.\n\nSubmitted - 0107140.pdf
", "abstract": "The hybrid formalism is used to quantize the superstring compactified to two-dimensional target-space in a manifestly spacetime supersymmetric manner. A quantizable sigma model action is then constructed for the type II superstring in curved two-dimensional supergravity backgrounds which can include Ramond\u2013Ramond flux. Such curved backgrounds include Calabi\u2013Yau four-fold compactifications with Ramond\u2013Ramond flux, and new extremal black hole solutions in two-dimensional dilaton supergravity theory. These black hole solutions are a natural generalization of the CGHS model and might be possible to describe using a supergroup version of the SL(2,R)/U(1) WZW model. We also study some dynamical aspects of the new black holes, such as formation and evaporation.", "date": "2001-10-29", "date_type": "published", "publication": "Nuclear Physics B", "volume": "614", "number": "1-2", "publisher": "Elsevier", "pagerange": "195-232", "id_number": "CaltechAUTHORS:20160506-075145513", "issn": "0550-3213", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160506-075145513", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico (CNPq)", "grant_number": "300256/94-9" }, { "agency": "Pronex", "grant_number": "66.2002/1998-9" }, { "agency": "Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de Sao Paulo (FAPESP)", "grant_number": "99/12763-0" }, { "agency": "Clay Mathematics Institute" }, { "agency": "Caltech Discovery Fund" }, { "agency": "NSF", "grant_number": "PHY99-07949" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "01-02-17488" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "00-15-99296" }, { "agency": "Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de Sao Paulo (FAPESP)", "grant_number": "00/02230-3" } ] }, "doi": "10.1016/S0550-3213(01)00413-8", "primary_object": { "basename": "0107140.pdf", "url": "https://authors.library.caltech.edu/records/a7jkf-bgb64/files/0107140.pdf" }, "resource_type": "article", "pub_year": "2001", "author_list": "Berkovits, Nathan; Gukov, Sergei; et el." }, { "id": "https://authors.library.caltech.edu/records/9rkq1-7ay51", "eprint_id": 66711, "eprint_status": "archive", "datestamp": "2023-08-19 08:17:56", "lastmod": "2023-10-18 18:44:05", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Brandhuber-A", "name": { "family": "Brandhuber", "given": "Andreas" } }, { "id": "Gomis-J", "name": { "family": "Gomis", "given": "Jaume" } }, { "id": "Gubser-S-S", "name": { "family": "Gubser", "given": "Steven S." } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" } ] }, "title": "Gauge theory at large N and new G\u2082 holonomy metrics", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2001 Elsevier Science B.V. \n\nReceived 14 June 2001, Accepted 16 July 2001, Available online 24 September 2001. \n\nWe are grateful to Michael Atiyah, Vadim Borokhov, Mirjam Cvetic, Igor Klebanov, Chris Pope, and especially Cumrun Vafa and Edward Witten for useful discussions. The work of A. Brandhuber and S. Gubser is supported in part by the DOE under grant No.DE-FG03-92ER40701. The work of J. Gomis is supported in part by the National Science Foundation under grant No. PHY99-07949 and by the DOE under grant No. DE-FG03-92ER40701. The research of S. Gukov is supported in part by the Caltech Discovery Fund, NSF grant No. PHY99-07949, grant RFBR No. 01-01-00549, and the Russian President's grant No. 00-15-99296.\n\nSubmitted - 0106034.pdf
", "abstract": "We find a one-parameter family of new G\u2082 holonomy metrics and demonstrate that it can be extended to a two-parameter family. These metrics play an important role as the supergravity dual of the large N limit of four-dimensional supersymmetric Yang\u2013Mills. We show that these G\u2082 holonomy metrics describe the M theory lift of the supergravity solution describing a collection of D6-branes wrapping the supersymmetric three-cycle of the deformed conifold geometry for any value of the string coupling constant.", "date": "2001-09-17", "date_type": "published", "publication": "Nuclear Physics B", "volume": "611", "number": "1-3", "publisher": "Elsevier", "pagerange": "179-204", "id_number": "CaltechAUTHORS:20160506-081903900", "issn": "0550-3213", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160506-081903900", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92ER40701" }, { "agency": "NSF", "grant_number": "PHY99-07949" }, { "agency": "Caltech Discovery Fund" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "01-01-00549" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "00-15-99296" } ] }, "doi": "10.1016/S0550-3213(01)00340-6", "primary_object": { "basename": "0106034.pdf", "url": "https://authors.library.caltech.edu/records/9rkq1-7ay51/files/0106034.pdf" }, "resource_type": "article", "pub_year": "2001", "author_list": "Brandhuber, Andreas; Gomis, Jaume; et el." }, { "id": "https://authors.library.caltech.edu/records/2vjph-9y185", "eprint_id": 3253, "eprint_status": "archive", "datestamp": "2023-08-21 22:22:11", "lastmod": "2023-10-16 15:45:15", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gubser-S-S", "name": { "family": "Gubser", "given": "S. S." } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "S." }, "orcid": "0000-0002-9486-1762" }, { "id": "Klebanov-I-R", "name": { "family": "Klebanov", "given": "I. R." } }, { "id": "Rangamani-Mukund", "name": { "family": "Rangamani", "given": "M." }, "orcid": "0000-0002-4336-1346" }, { "id": "Witten-E", "name": { "family": "Witten", "given": "E." }, "orcid": "0000-0002-7752-6073" } ] }, "title": "The Hagedorn transition in noncommutative open string theory", "ispublished": "pub", "full_text_status": "public", "keywords": "string theory; differential geometry; membrane theory; gauge field theory", "note": "\u00a92001 American Institute of Physics. \n\n(Received 2 January 2001; accepted 13 February 2001) \n\nWe are grateful to J. Maldacena, E. Rabinovici, and S. Shenker for useful discussions. The work of S.S.G. was supported in part by Department of Energy (DOE) Grant No. DE-FG02-91ER40671, and by a DOE Outstanding Junior Investigator award. The work of S.G. was supported in part by the Caltech Discovery Fund, Grant No. RFBR No. 98-02-16575 and Russian President's Grant No. No 96-15-96939. The work of I.R.K. was supported in part by the National Science Foundation (NSF) Grant No. PHY-9802484 and by the James S. McDonnell Foundation Grant No. 91-48. M.R. was supported in part by NSF Grant No. PHY-980248 and by the Caltech Discovery Fund. S.S.G. and I.R.K. thank the Aspen Center for Physics for hospitality while this work was in progress.\n\nPublished - GUBjmp01.pdf
", "abstract": "The Hagedorn transition in noncommutative open string theory (NCOS) is relatively simple because gravity decouples. For NCOS theories in no more than five space\u2013time dimensions, the Hagedorn transition is second order, and the high temperature phase involves long, nearly straight fundamental strings separating from the D-brane on which the NCOS theory is defined. Above five spacetime dimensions interaction effects become important below the Hagedorn temperature. Although this complicates studies of the transition, we believe that the high temperature phase again involves long strings liberated from the bound state.", "date": "2001-07", "date_type": "published", "publication": "Journal of Mathematical Physics", "volume": "42", "number": "7", "publisher": "American Institute of Physics", "pagerange": "2749-2764", "id_number": "CaltechAUTHORS:GUBjmp01", "issn": "0022-2488", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:GUBjmp01", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG02-91ER40671" }, { "agency": "Caltech Discovery Fund" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "98-02-16575" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "96-15-96939" }, { "agency": "NSF", "grant_number": "PHY-9802484" }, { "agency": "James S. McDonnell Foundation", "grant_number": "91-48" }, { "agency": "NSF", "grant_number": "PHY-980248" } ] }, "doi": "10.1063/1.1372176", "primary_object": { "basename": "GUBjmp01.pdf", "url": "https://authors.library.caltech.edu/records/2vjph-9y185/files/GUBjmp01.pdf" }, "resource_type": "article", "pub_year": "2001", "author_list": "Gubser, S. S.; Gukov, S.; et el." }, { "id": "https://authors.library.caltech.edu/records/36wk3-ahr50", "eprint_id": 66698, "eprint_status": "archive", "datestamp": "2023-08-21 22:14:39", "lastmod": "2023-10-18 18:43:13", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Behrndt-K", "name": { "family": "Behrndt", "given": "Klaus" } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Shmakova-M", "name": { "family": "Shmakova", "given": "Marina" } } ] }, "title": "Domain walls, black holes, and supersymmetric quantum mechanics", "ispublished": "pub", "full_text_status": "public", "keywords": "Domain walls; Black holes; Supergravity; Supersymmetric vacua; AdS/CFT", "note": "\u00a9 2001 Elsevier Science B.V. \n\nReceived 2 February 2001, Accepted 7 February 2001, Available online 25 April 2001. \n\nWe are grateful Alexander Chervov, Ori Ganor, Brian Greene, Renata Kallosh, Eric Sharpe, Gary Shiu, Andrew Strominger, Nicholas Warner, and Edward Witten for helpful discussions and comments. The work of K.B. was partly done at the Theory group of Caltech and is supported by a Heisenberg grant of the DFG and by the European Commission RTN programme HPRN-CT-2000-00131. S.G. is supported in part by the Caltech Discovery Fund, grant RFBR No 98-01-00327 and Russian President's grant No 00-15-99296.\n\nSubmitted - 0101119.pdf
", "abstract": "Supersymmetric solutions, such as BPS domain walls or black holes, in four- and five-dimensional supergravity theories with eight supercharges can be described by effective quantum mechanics with a potential term. We show how properties of the latter theory can help us to learn about the physics of supersymmetric vacua and BPS solutions in these supergravity theories. The general approach is illustrated in a number of specific examples where scalar fields of matter multiplets take values in symmetric coset spaces.", "date": "2001-05-07", "date_type": "published", "publication": "Nuclear Physics B", "volume": "601", "number": "1-2", "publisher": "Elsevier", "pagerange": "49-76", "id_number": "CaltechAUTHORS:20160505-151644609", "issn": "0550-3213", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160505-151644609", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Deutsche Forschungsgemeinschaft (DFG)" }, { "agency": "European Union", "grant_number": "HPRN-CT-2000-00131" }, { "agency": "Caltech Discovery Fund" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "98-01-00327" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "00-15-99296" } ] }, "doi": "10.1016/S0550-3213(01)00052-9", "primary_object": { "basename": "0101119.pdf", "url": "https://authors.library.caltech.edu/records/36wk3-ahr50/files/0101119.pdf" }, "resource_type": "article", "pub_year": "2001", "author_list": "Behrndt, Klaus; Gukov, Sergei; et el." }, { "id": "https://authors.library.caltech.edu/records/8a4b0-eg244", "eprint_id": 66696, "eprint_status": "archive", "datestamp": "2023-08-19 06:20:23", "lastmod": "2023-10-18 18:43:04", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gates-S-J-Jr", "name": { "family": "Gates", "given": "S. James, Jr." } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Witten-E", "name": { "family": "Witten", "given": "Edward" }, "orcid": "0000-0002-7752-6073" } ] }, "title": "Two two-dimensional supergravity theories from Calabi\u2013Yau four-folds", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2000 Elsevier Science B.V. \n\nReceived 25 May 2000, Accepted 13 June 2000, Available online 21 August 2000. \n\nWe are grateful to Marc Grisaru, Martin Ro\u010dek and John H. Schwarz for useful discussions. The research of S.J.G. is supported by the NSF grant No PHY-98-02551; S.G. is supported in part by the Caltech Discovery Fund, grant RFBR No 98-02-16575 and Russian President's grant No 96-15-96939. The work of E.W. is supported in part by NSF Grant PHY-9513835 and the Caltech Discovery Fund.\n\nSubmitted - 0005120.pdf
", "abstract": "We consider two-dimensional supergravity theories with four supercharges constructed from compactification of Type II string theory on a generic Calabi\u2013Yau four-fold. In type IIA and type IIB cases, respectively, new superspace formulations of N = (2, 2) and N = (0,4) dilaton supergravities are found and their coupling to matter multiplets is discussed.", "date": "2000-09-18", "date_type": "published", "publication": "Nuclear Physics B", "volume": "584", "number": "1-2", "publisher": "Elsevier", "pagerange": "109-148", "id_number": "CaltechAUTHORS:20160505-142923299", "issn": "0550-3213", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160505-142923299", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-98-02551" }, { "agency": "Caltech Discovery Fund" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "98-02-16575" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "96-15-96939" }, { "agency": "NSF", "grant_number": "PHY-9513835" } ] }, "doi": "10.1016/S0550-3213(00)00374-6", "primary_object": { "basename": "0005120.pdf", "url": "https://authors.library.caltech.edu/records/8a4b0-eg244/files/0005120.pdf" }, "resource_type": "article", "pub_year": "2000", "author_list": "Gates, S. James, Jr.; Gukov, Sergei; et el." }, { "id": "https://authors.library.caltech.edu/records/amssh-7bb44", "eprint_id": 66641, "eprint_status": "archive", "datestamp": "2023-08-21 21:24:34", "lastmod": "2023-10-18 18:39:31", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Behrndt-K", "name": { "family": "Behrndt", "given": "Klaus" } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" } ] }, "title": "Domain walls and superpotentials from M-theory on Calabi-Yau three-folds", "ispublished": "pub", "full_text_status": "public", "keywords": "M-theory; Superpotential; Domain wall", "note": "\u00a9 2000 Elsevier Science B.V. \n\nWe would like to thank K. & M. Becker, J. Gomis, C. Vafa and E. Witten for useful discussions. The work of K.B. was supported by a Heisenberg Fellowship of the DFG. The work of S.G. was supported in part by the Caltech Discovery Fund, grant RFBR No 98-02-16575 and Russian President's grant No 96-15-96939.\n\nSubmitted - 0001082.pdf
", "abstract": "Compactification of M-theory in the presence of G-fluxes yields N = 2 five-dimensional gauged supergravity with a potential that lifts all supersymmetric vacua. We derive the effective superpotential directly from the Kaluza\u2013Klein reduction of the eleven-dimensional action on a Calabi\u2013Yau three-fold and compare it with the superpotential obtained by means of calibrations. We discuss an explicit domain wall solution, which represents five-branes wrapped over holomorphic cycles. This solution has a \"running volume\" and we comment on the possibility that quantum corrections provide a lower bound allowing for an AdS\u2085 vacuum of the 5-dimensional supergravity.", "date": "2000-07-31", "date_type": "published", "publication": "Nuclear Physics B", "volume": "580", "number": "1-2", "publisher": "Elsevier", "pagerange": "225-242", "id_number": "CaltechAUTHORS:20160504-100830938", "issn": "0550-3213", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160504-100830938", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Deutsche Forschungsgemeinschaft (DFG)" }, { "agency": "Caltech Discovery Fund" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "98-02-16575" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "96-15-96939" } ] }, "doi": "10.1016/S0550-3213(00)00149-8", "primary_object": { "basename": "0001082.pdf", "url": "https://authors.library.caltech.edu/records/amssh-7bb44/files/0001082.pdf" }, "resource_type": "article", "pub_year": "2000", "author_list": "Behrndt, Klaus and Gukov, Sergei" }, { "id": "https://authors.library.caltech.edu/records/y88jt-v0y64", "eprint_id": 67061, "eprint_status": "archive", "datestamp": "2023-08-21 21:20:27", "lastmod": "2023-10-18 19:55:27", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Periwal-V", "name": { "family": "Periwal", "given": "Vipul" } } ] }, "title": "Dbrane phase transitions and monodromy in K-theory", "ispublished": "pub", "full_text_status": "public", "keywords": "Dbranes; K-theory", "note": "\u00a9 2000 Elsevier Science B.V. \n\nReceived 21 September 1999, Available online 1 June 2000. \n\nWe have benefited from discussions with R. Bezrukavnikov, M. Kontsevich, J. Rosenberg, A. Schwarz, A. Sen, E. Sharpe and E. Witten. The work of S.G. was supported in part by grant RFBR No. 98-02-16575 and Russian President's grant No 96-15-96939. The work of V.P. was supported in part by NSF grant PHY-9802484.\n\nSubmitted - 9908166.pdf
", "abstract": "Majumder and Sen have given an explicit construction of a first order phase transition in a non-supersymmetric system of Dbranes that occurs when the B-field is varied. We show that the description of this transition in terms of K-theory involves a bundle of K groups of non-commutative algebras over the K\u00e4hler cone with nontrivial monodromy. Thus the study of monodromy in K groups associated with quantized algebras can be used to predict the phase structure of systems of (non-supersymmetric) Dbranes.", "date": "2000-07", "date_type": "published", "publication": "Journal of Geometry and Physics", "volume": "34", "number": "3-4", "publisher": "Elsevier", "pagerange": "263-269", "id_number": "CaltechAUTHORS:20160513-082826792", "issn": "0393-0440", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160513-082826792", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Russian Foundation for Basic Research", "grant_number": "98-02-16575" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "96-15-96939" }, { "agency": "NSF", "grant_number": "PHY-9802484" } ] }, "doi": "10.1016/S0393-0440(99)00067-4", "primary_object": { "basename": "9908166.pdf", "url": "https://authors.library.caltech.edu/records/y88jt-v0y64/files/9908166.pdf" }, "resource_type": "article", "pub_year": "2000", "author_list": "Gukov, Sergei and Periwal, Vipul" }, { "id": "https://authors.library.caltech.edu/records/6ec67-rew47", "eprint_id": 66995, "eprint_status": "archive", "datestamp": "2023-08-19 05:46:45", "lastmod": "2023-10-18 19:50:20", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" } ] }, "title": "Solitons, superpotentials and calibrations", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2000 Elsevier Science B.V. \n\nI would like to express my gratitude to S. James Gates and especially to Edward Witten for helpful discussions and constant encouragement. The work was supported in part by the Caltech Discovery Fund, grant RFBR No 98-02-16575 and Russian President's grant No 96-15-96939.\n\nSubmitted - 9911011.pdf
", "abstract": "In this paper we study several issues related to the generation of the superpotential induced by background Ramond\u2013Ramond fluxes in compactification of Type IIA string theory on Calabi\u2013Yau four-folds. Identifying BPS solitons with D-branes wrapped over calibrated submanifolds in a Calabi\u2013Yau space, we propose a general formula for the superpotential and justify it comparing the supersymmetry conditions in D=2 and D=10 supergravity theories. We also suggest a geometric interpretation to the supersymmetric index in the two-dimensional effective theory in terms of topological invariants of the Calabi\u2013Yau four-fold, and estimate the asymptotic growth of these invariants from BTZ black hole entropy. Finally, we explicitly construct new supersymmetric vacua for Type IIA string theory compactification on a Calabi\u2013Yau four-fold with Ramond\u2013Ramond fluxes.", "date": "2000-05-15", "date_type": "published", "publication": "Nuclear Physics B", "volume": "574", "number": "1-2", "publisher": "Elsevier", "pagerange": "169-188", "id_number": "CaltechAUTHORS:20160511-131311298", "issn": "0550-3213", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160511-131311298", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Caltech Discovery Fund" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "98-02-16575" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "96-15-96939" } ] }, "doi": "10.1016/S0550-3213(00)00053-5", "primary_object": { "basename": "9911011.pdf", "url": "https://authors.library.caltech.edu/records/6ec67-rew47/files/9911011.pdf" }, "resource_type": "article", "pub_year": "2000", "author_list": "Gukov, Sergei" }, { "id": "https://authors.library.caltech.edu/records/ex9w5-bc783", "eprint_id": 66989, "eprint_status": "archive", "datestamp": "2023-08-19 05:35:17", "lastmod": "2023-10-18 19:49:53", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" } ] }, "title": "K-Theory, Reality, and Orientifolds", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2000 Springer-Verlag. \n\nReceived: 9 March 1999; Accepted: 15 October 1999. \n\nI am very grateful to C. Bachas,W. Browder, M. J. Hopkins, I. R. Klebanov, S. Martin, A. Schwarz and especially to E. Witten for interesting and illuminating discussions/correspondence. It is pleasure to thank Harvard University for financial support and hospitality while the manuscript was being completed. The work was supported in part by grant RFBR No 98-02-16575 and Russian President's grant No 96-15-96939.\n\nSubmitted - 9901042.pdf
", "abstract": "We use equivariant K-theory to classify charges of new (possibly non-supersymmetric) states localized on various orientifolds in Type II string theory. We also comment on the stringy construction of new D-branes and demonstrate the discrete electric-magnetic duality in Type I brane systems with p+q=7, as proposed by Witten.", "date": "2000-04", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "210", "number": "3", "publisher": "Springer", "pagerange": "621-639", "id_number": "CaltechAUTHORS:20160511-110549355", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160511-110549355", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Harvard University" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "98-02-16575" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "96-15-96939" } ] }, "doi": "10.1007/s002200050793", "primary_object": { "basename": "9901042.pdf", "url": "https://authors.library.caltech.edu/records/ex9w5-bc783/files/9901042.pdf" }, "resource_type": "article", "pub_year": "2000", "author_list": "Gukov, Sergei" }, { "id": "https://authors.library.caltech.edu/records/j9tn4-95w04", "eprint_id": 67063, "eprint_status": "archive", "datestamp": "2023-08-22 13:43:28", "lastmod": "2023-10-18 19:55:38", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" } ] }, "title": "New N = 2 superconformal field theories from M/F-theory orbifolds", "ispublished": "pub", "full_text_status": "public", "keywords": "Gauge theory; M-theory; F-theory", "note": "\u00a9 1999 Elsevier B.V. \n\nReceived 13 November 1998, Accepted 7 January 1999, Available online 1 July 1999. \n\nThe authors wish to thank O. Aharony, M. Berkooz, and E. Witten for helpful discussions. The work of S.G. was supported in part by NSF grant PHY-9802484, RFBR grant No 98-02-16575, and Russian President's grant No 96-15-96939. The work of A.K. was supported in part by DOE grant DE-FG02-90-ER40542.\n\nSubmitted - 9808175.pdf
", "abstract": "We consider M-theory on (T^2 \u00d7 R^2)/Zn with M5-branes wrapped on R^2 One can probe this background with M5-branes wrapped on T2. The theories on the probes provide many new examples of N = 2 field theories without Lagrangian description. All these theories have Coulomb branches, and we find the corresponding Seiberg-Witten curves. The exact solution is encoded in a Hitchin system on an orbifolded torus with punctures. The theories we consider also arise from D3 probes in F-theory on K3 \u00d7 K3 orbifolds. Interestingly, the relevant F-theory background has frozen Z_n singularities which are analogous to frozen Z_2 singularities in Type I string theory. We use the F-theory description to find supergravity duals of the probe SCFT's in the large-N limit and compute the spectrum of relevant and marginal operators. We also explain how the decoupling of U(1) factors is manifested in the supergravity description.", "date": "1999-04-19", "date_type": "published", "publication": "Nuclear Physics B", "volume": "545", "number": "1-3", "publisher": "Elsevier", "pagerange": "283-308", "id_number": "CaltechAUTHORS:20160513-090539528", "issn": "0550-3213", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160513-090539528", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-9802484" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "98-02-16575" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "96-15-96939" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG02-90-ER40542" } ] }, "doi": "10.1016/S0550-3213(99)00008-5", "primary_object": { "basename": "9808175.pdf", "url": "https://authors.library.caltech.edu/records/j9tn4-95w04/files/9808175.pdf" }, "resource_type": "article", "pub_year": "1999", "author_list": "Gukov, Sergei and Kapustin, Anton" }, { "id": "https://authors.library.caltech.edu/records/tzt67-td904", "eprint_id": 66991, "eprint_status": "archive", "datestamp": "2023-08-22 13:20:16", "lastmod": "2023-10-18 19:50:07", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Diaconescu-D-E", "name": { "family": "Diaconescu", "given": "Duiliu-Emanuel" } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" } ] }, "title": "Three-dimensional N = 2 gauge theories and degenerations of Calabi-Yau four-folds", "ispublished": "pub", "full_text_status": "public", "keywords": "Four-folds; Gauge theories; Degenerations", "note": "\u00a9 1998 Elsevier B.V. \n\nWe are very grateful to Cumrun Vafa and Edward Witten for collaboration and valuable suggestions and to Liviu Nicolaescu for mathematical assistance. We would also like to thank Ofer Aharony, Tom Banks, Jan de Boer, Michael Douglas, Rami Entin, Ori Ganor, Jaume Gomis, Brian Greene, Barak Kol, Wolfgang Lerche, Nathan Seiberg and Piljin Yi for very helpful discussions and correspondence. S.G also would like to thank Laboratoire de Physique Th\u00e9orique et Hautes Energies where a part of this work was done, and especially L. Baulieu for kind hospitality and the support of the CNRS grant. The research of S. G. was supported in part by Merit Fellowship in Natural Sciences and Mathematics, grant RFBR-96-15-96939 and CNRS Foundation.\n\nSubmitted - 9804059.pdf
", "abstract": "Three-dimensional N = 2 gauge theories with arbitrary gauge group and fundamental flavors are engineered from degenerations of Calabi-Yau four-folds. We show how Coulomb and Higgs branches emerge in the geometric picture. The analysis of instanton generated superpotentials unravels interesting aspects of the five-brane effective action in M-theory.", "date": "1998-12-07", "date_type": "published", "publication": "Nuclear Physics B", "volume": "535", "number": "1-2", "publisher": "Elsevier", "pagerange": "171-196", "id_number": "CaltechAUTHORS:20160511-111658565", "issn": "0550-3213", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160511-111658565", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Merit Fellowship in Natural Sciences and Mathematics" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "96-15-96939" }, { "agency": "Centre National de la Recherche Scientifique (CNRS)" } ] }, "doi": "10.1016/S0550-3213(98)00597-5", "primary_object": { "basename": "9804059.pdf", "url": "https://authors.library.caltech.edu/records/tzt67-td904/files/9804059.pdf" }, "resource_type": "article", "pub_year": "1998", "author_list": "Diaconescu, Duiliu-Emanuel and Gukov, Sergei" }, { "id": "https://authors.library.caltech.edu/records/jpk1h-cwr62", "eprint_id": 2016, "eprint_status": "archive", "datestamp": "2023-08-22 13:18:15", "lastmod": "2023-10-13 23:09:09", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Rangamani-Mukund", "name": { "family": "Rangamani", "given": "Mukund" }, "orcid": "0000-0002-4336-1346" }, { "id": "Witten-E", "name": { "family": "Witten", "given": "Edward" }, "orcid": "0000-0002-7752-6073" } ] }, "title": "Dibaryons, branes, and strings in AdS orbifold models", "ispublished": "pub", "full_text_status": "public", "keywords": "Duality in Gauge Field Theories, Superstring Vacua, Brane Dynamics in Gauge Theories", "note": "\u00a9 Institute of Physics 1998 \n\nReceived 25 November 1998, accepted for publication 26 December 1998, Published 9 March 1999 \n\nIt is pleasure to thank to M. Krogh, S.N. Minwalla, and A. Mikhailov, for helpful discussions and N. Nekrasov for collaboration in an early stage of the project. The work of S.G. was supported in part by grant RFBR No 98-02-16575 and Russian President's grant No 96-15-96939. The work of E.W. is supported in part by NSF Grant PHY-9513835 and that of M.R. by NSF Grant PHY-9802484.\n\nPublished - GUKjhep98.pdf
", "abstract": "A generalization of the Maldacena conjecture asserts that Type IIB string theory on AdS5 \u00d7 S5/Bbb Z3 is equivalent to a certain supersymmetric SU(N)3 gauge theory with bifundamental matter. To test this assertion, we analyze the wrapped branes on S5/Bbb Z3 and their interpretation in terms of gauge theory. The wrapped branes are interpreted in some cases as baryons or dibaryons of the gauge theory and in other cases as strings around which there is a global monodromy. In order to successfully match the brane analysis with field theory, we must uncover some aspects of S-duality which are novel even in the case of four-dimensional free field theory.", "date": "1998-12", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "1998", "number": "12", "publisher": "Springer", "pagerange": "Art. No. 025", "id_number": "CaltechAUTHORS:GUKjhep98", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:GUKjhep98", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Russian Foundation for Basic Research", "grant_number": "98-02-16575" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "96-15-96939" }, { "agency": "NSF", "grant_number": "PHY-9513835" }, { "agency": "NSF", "grant_number": "PHY-9802484" } ] }, "doi": "10.1088/1126-6708/1998/12/025", "primary_object": { "basename": "GUKjhep98.pdf", "url": "https://authors.library.caltech.edu/records/jpk1h-cwr62/files/GUKjhep98.pdf" }, "resource_type": "article", "pub_year": "1998", "author_list": "Gukov, Sergei; Rangamani, Mukund; et el." }, { "id": "https://authors.library.caltech.edu/records/y1zq4-srm92", "eprint_id": 67072, "eprint_status": "archive", "datestamp": "2023-08-19 03:26:56", "lastmod": "2023-10-18 19:56:22", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" } ] }, "title": "Comments on N = S AdS orbifolds", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1998 Elsevier Science B.V. \n\nReceived 7 July 1998, Available online 21 November 1998. \n\nEditor: P.V. Landshoff. \n\nI am grateful to M. Berkooz, O.J. Ganor, J. Gomis, A. Mikhailov, Y. Oz, M. J. Strassler and A.M. Uranga for helpful conversations. Especially I would like to thank E. Witten for suggesting the problem and stimulating discussions. The work was supported in part by Merit Fellowship in Natural Sciences and Mathematics and grant RFBR No 98-02-16575 and Russian President's grant No 96-15-96939.\n\nSubmitted - 9806180.pdf
", "abstract": "We discuss twisted states of AdS orbifolds which couple to N = 2 chiral primary operators not invariant under exchange of the gauge factors. Kaluza-Klein reduction on the fixed circle gives the correct conformal dimensions of operators in the superconformal theory and involves some aspects of monopole dynamics in the non-trivial background. As a byproduct we found evidence for decoupling of U(1) factors in the four-dimensional gauge theory.", "date": "1998-10-29", "date_type": "published", "publication": "Physics Letters B", "volume": "439", "number": "1-2", "publisher": "Elsevier", "pagerange": "23-28", "id_number": "CaltechAUTHORS:20160513-103122668", "issn": "0370-2693", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160513-103122668", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Russian Foundation for Basic Research", "grant_number": "98-02-16575" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "96-15-96939" } ] }, "doi": "10.1016/S0370-2693(98)01005-3", "primary_object": { "basename": "9806180.pdf", "url": "https://authors.library.caltech.edu/records/y1zq4-srm92/files/9806180.pdf" }, "resource_type": "article", "pub_year": "1998", "author_list": "Gukov, Sergei" }, { "id": "https://authors.library.caltech.edu/records/znh2s-jxj39", "eprint_id": 66988, "eprint_status": "archive", "datestamp": "2023-08-19 01:12:16", "lastmod": "2023-10-18 19:49:49", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "S." }, "orcid": "0000-0002-9486-1762" } ] }, "title": "Supersymmetric spin glass", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1997 American Institute of Physics. \n\nSubmitted 27 February 1997; resubmitted 4 April 1997. \n\nThis work was supported in part by the Russian Fund for Fundamental Research, Grant No. 96-15-96939.\n\nPublished - art_3A10.1134_2F1.567408.pdf
Submitted - 9702063.pdf
", "abstract": "The manifestly supersymmetric four-dimensional Wess-Zumino model with quenched disorder is considered at the one-loop level. The infrared fixed points of a beta function form the moduli space \u2133=RP^2, where two types of phases are found: with and without replica symmetry. While the former phase possesses only a trivial fixed point, this point become unstable in the latter phase, which may be interpreted as a spin glass phase.", "date": "1997-04", "date_type": "published", "publication": "Journal of Experimental and Theoretical Physics Letters", "volume": "65", "number": "8", "publisher": "American Institute of Physics", "pagerange": "694-700", "id_number": "CaltechAUTHORS:20160511-105722161", "issn": "0021-3640", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160511-105722161", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Russian Fund for Fundamental Research", "grant_number": "96-15-96939" } ] }, "collection": "CaltechAUTHORS", "doi": "10.1134/1.567408", "primary_object": { "basename": "9702063.pdf", "url": "https://authors.library.caltech.edu/records/znh2s-jxj39/files/9702063.pdf" }, "related_objects": [ { "basename": "art_3A10.1134_2F1.567408.pdf", "url": "https://authors.library.caltech.edu/records/znh2s-jxj39/files/art_3A10.1134_2F1.567408.pdf" } ], "resource_type": "article", "pub_year": "1997", "author_list": "Gukov, S." }, { "id": "https://authors.library.caltech.edu/records/0sc38-d2v59", "eprint_id": 67071, "eprint_status": "archive", "datestamp": "2023-08-19 00:57:41", "lastmod": "2023-10-18 19:56:17", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Polyubin-I", "name": { "family": "Polyubin", "given": "Igor" } } ] }, "title": "Related N = 2 SUSY Yang Mills Theories and Instanton Expansion", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1997 Published by Elsevier. \n\nReceived 23 August 1996, Revised 25 October 1996, Available online 14 May 1998. \n\nWe are indebted to A. Morozov for helpful discussions and comments. S. Gukov would like to thank A. Mironov and S. Khoroshkin for teaching him some useful mathematical background. I. Polyubin is grateful to the Institute of Theoretical Physics at Hannover for kind hospitality where part of this work was done. \n\nThe work of S.G. was partially supported by RFBR grant No. 95-01-00755, the work of I.P. by grants RFBR-96-01-01106 and INTAS-93-1038. I. Polyubin also would like to thank Volkswagen Stiftung project \"Integrable models and strings\" for financial support.\n\nSubmitted - 9607169.pdf
", "abstract": "The low energy effective actions of the N = 2 SUSY SU(N_c) QCD are considered at the symmetric point on the moduli space. The classes of such theories have similar spectral curves. This fact allows us to show that all these models have the same structure of the coupling matrix and to show that the N_f = 2N_c spectral curve can not be presented as a double covering of the sphere. We calculate first instanton contributions to the coupling matrix and get nonperturbative \u03b2-functions in the SU(2) gauge theory with non-zero bare masses of the matter hypermultiplets.", "date": "1997-01-09", "date_type": "published", "publication": "Physics Letters B", "volume": "391", "number": "1-2", "publisher": "Elsevier", "pagerange": "115-123", "id_number": "CaltechAUTHORS:20160513-101814510", "issn": "0370-2693", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160513-101814510", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Russian Foundation for Basic Research", "grant_number": "95-01-00755" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "RFBR-96-01-01106" }, { "agency": "International Association for Cooperation with Scientifics (INTAS)", "grant_number": "INTAS-93-1038" }, { "agency": "Volkswagen Stiftung" } ] }, "collection": "CaltechAUTHORS", "doi": "10.1016/S0370-2693(96)01454-2", "primary_object": { "basename": "9607169.pdf", "url": "https://authors.library.caltech.edu/records/0sc38-d2v59/files/9607169.pdf" }, "resource_type": "article", "pub_year": "1997", "author_list": "Gukov, Sergei and Polyubin, Igor" } ]