[ { "id": "authors:w9vm2-wpd47", "collection": "authors", "collection_id": "w9vm2-wpd47", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20220816-192438269", "type": "monograph", "title": "Near-Horizon Quantum Dynamics of 4-d Einstein Gravity from 2-d JT Gravity", "author": [ { "family_name": "Gukov", "given_name": "Sergei", "orcid": "0000-0002-9486-1762", "clpid": "Gukov-S" }, { "family_name": "Lee", "given_name": "Vincent S. H.", "clpid": "Lee-Vincent-S-H" }, { "family_name": "Zurek", "given_name": "Kathryn M.", "orcid": "0000-0002-2629-337X", "clpid": "Zurek-K-M" } ], "abstract": "We study quantum fluctuations in the lightcone metric of the 4-d 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 4-d 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 4-d 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.", "doi": "10.48550/arXiv.2205.02233", "publisher": "arXiv", "publication_date": "2022-05-04" }, { "id": "authors:ygk81-2jx08", "collection": "authors", "collection_id": "ygk81-2jx08", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20211206-191012374", "type": "monograph", "title": "Symmetries of 2d TQFTs and Equivariant Verlinde Formulae for General Groups", "author": [ { "family_name": "Gukov", "given_name": "Sergei", "orcid": "0000-0002-9486-1762", "clpid": "Gukov-S" }, { "family_name": "Pei", "given_name": "Du", "orcid": "0000-0001-5587-6905", "clpid": "Pei-Du" }, { "family_name": "Reid", "given_name": "Charles", "orcid": "0000-0003-4598-5635", "clpid": "Reid-Charles" }, { "family_name": "Shehper", "given_name": "Ali", "orcid": "0000-0002-3440-1721", "clpid": "Shehper-Ali" } ], "abstract": "We study (generalized) discrete symmetries of 2d semisimple TQFTs. These are 2d TQFTs whose fusion rules can be diagonalized. We show that, in this special basis, the 0-form symmetries always act as permutations while 1-form symmetries act by phases. This leads to an explicit description of the gauging of these symmetries. One application of our results is a generalization of the equivariant Verlinde formula to the case of general Lie groups. The generalized formula leads to many predictions for the geometry of Hitchin moduli spaces, which we explicitly check in several cases with low genus and SO(3) gauge group.", "publisher": "arXiv", "publication_date": "2021-11-15" }, { "id": "authors:7p4y5-z2m03", "collection": "authors", "collection_id": "7p4y5-z2m03", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170518-093106050", "type": "monograph", "title": "Vertex algebras and 4-manifold invariants", "author": [ { "family_name": "Dedushenko", "given_name": "Mykola", "orcid": "0000-0002-9273-7602", "clpid": "Dedushenko-M" }, { "family_name": "Gukov", "given_name": "Sergei", "orcid": "0000-0002-9486-1762", "clpid": "Gukov-S" }, { "family_name": "Putrov", "given_name": "Pavel", "clpid": "Putrov-P" } ], "abstract": "We propose a way of computing 4-manifold invariants, old and new, as chiral\ncorrelation functions in half-twisted 2d N = (0, 2) theories that arise from compactification of fivebranes. Such formulation gives a new interpretation of some known statements\nabout Seiberg-Witten invariants, such as the basic class condition, and gives a prediction\nfor structural properties of the multi-monopole invariants and their non-abelian generalizations.", "doi": "10.48550/arXiv.1705.01645", "publisher": "arXiv", "publication_date": "2017-05-03" }, { "id": "authors:9deyp-p1157", "collection": "authors", "collection_id": "9deyp-p1157", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160816-123626732", "type": "monograph", "title": "The Verlinde formula for Higgs bundles", "author": [ { "family_name": "Andersen", "given_name": "J\u00f8rgen Ellegaard", "orcid": "0000-0001-9721-0722", "clpid": "Andersen-J-E" }, { "family_name": "Gukov", "given_name": "Sergei", "orcid": "0000-0002-9486-1762", "clpid": "Gukov-S" }, { "family_name": "Pei", "given_name": "Du", "orcid": "0000-0001-5587-6905", "clpid": "Pei-Du" } ], "abstract": "We propose and prove the Verlinde formula for the quantization of the Higgs\nbundle moduli spaces and stacks for any simple and simply-connected group. This\ngeneralizes the equivariant Verlinde formula for the case of SU(n) proposed\npreviously by the second and third author. We further establish a Verlinde\nformula for the quantization of parabolic Higgs bundle moduli spaces and\nstacks.", "doi": "10.48550/arXiv.1608.01761", "publisher": "arXiv", "publication_date": "2016-08-05" }, { "id": "authors:0xpnc-07837", "collection": "authors", "collection_id": "0xpnc-07837", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160707-134251692", "type": "monograph", "title": "Resurgence in complex Chern-Simons theory", "author": [ { "family_name": "Gukov", "given_name": "Sergei", "orcid": "0000-0002-9486-1762", "clpid": "Gukov-S" }, { "family_name": "Marino", "given_name": "Marcos", "clpid": "Marino-M" }, { "family_name": "Putrov", "given_name": "Pavel", "clpid": "Putrov-P" } ], "abstract": "We study resurgence properties of partition function of SU(2) Chern-Simons\ntheory (WRT invariant) on closed three-manifolds. We check explicitly that in\nvarious examples Borel transforms of asymptotic expansions posses expected\nanalytic properties. In examples that we study we observe that contribution of\nirreducible flat connections to the path integral can be recovered from\nasymptotic expansions around abelian flat connections. We also discuss\nconnection to Floer instanton moduli spaces, disk instantons in 2d sigma models, and length spectra of \"complex geodesics\" on the A-polynomial curve.", "doi": "10.48550/arXiv.1605.07615", "publisher": "arXiv", "publication_date": "2016-05-24" }, { "id": "authors:25t19-ds637", "collection": "authors", "collection_id": "25t19-ds637", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20151207-102030601", "type": "monograph", "title": "Junctions of surface operators and categorification of quantum groups", "author": [ { "family_name": "Chun", "given_name": "Sungbong", "clpid": "Chun-Sungbong" }, { "family_name": "Gukov", "given_name": "Sergei", "orcid": "0000-0002-9486-1762", "clpid": "Gukov-S" }, { "family_name": "Roggenkamp", "given_name": "Daniel", "clpid": "Roggenkamp-D" } ], "abstract": "We show how networks of Wilson lines realize quantum groups U_q(sl_m), for arbitrary m, in 3d SU(N) Chern-Simons theory. Lifting this construction to foams of surface operators in 4d theory we find that rich structure of junctions is encoded in combinatorics of planar diagrams. For a particular choice of surface operators we reproduce known mathematical constructions of categorical representations and categorified quantum groups.", "doi": "10.48550/arXiv.1507.06318", "publication_date": "2015-07-22" }, { "id": "authors:v4xvz-91c74", "collection": "authors", "collection_id": "v4xvz-91c74", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160503-090914800", "type": "monograph", "title": "Duality Defects", "author": [ { "family_name": "Gadde", "given_name": "Abhijit", "clpid": "Gadde-A" }, { "family_name": "Gukov", "given_name": "Sergei", "orcid": "0000-0002-9486-1762", "clpid": "Gukov-S" }, { "family_name": "Putrov", "given_name": "Pavel", "clpid": "Putrov-P" } ], "abstract": "We propose a unified approach to a general class of codimension-2 defects in field theories with non-trivial duality symmetries and discuss various constructions of such \"duality defects\" in diverse dimensions. In particular, in d=4 we propose a new interpretation of the Seiberg-Witten u-plane by \"embedding\" it in the physical space-time: we argue that it describes a BPS configuration of two duality defects (at the monopole/dyon points) and propose its vast generalization based on Lefschetz fibrations of 4-manifolds.", "doi": "10.48550/arXiv.1404.2929", "publication_date": "2014-04-10" }, { "id": "authors:vtetj-feb46", "collection": "authors", "collection_id": "vtetj-feb46", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160503-094901740", "type": "monograph", "title": "Topological Quantum Field Theory, Nonlocal Operators, and Gapped Phases of Gauge Theories", "author": [ { "family_name": "Gukov", "given_name": "Sergei", "orcid": "0000-0002-9486-1762", "clpid": "Gukov-S" }, { "family_name": "Kapustin", "given_name": "Anton", "orcid": "0000-0003-3903-5158", "clpid": "Kapustin-A" } ], "abstract": "We revisit the role of loop and surface operators as order parameters for gapped phases of four-dimensional gauge theories. We show that in some cases surface operators are confined, and that this fact can be used to distinguish phases which are not distinguished by the Wilson-'t Hooft criterion. The long-distance behavior of loop and surface operators which are neither confined nor screened is controlled by a 4d TQFT. We construct these TQFTs for phases which are characterized by the presence of electrically and/or magnetically charged condensates. Interestingly, the TQFT describing a phase with a nonabelian monopole condensate is based on the theory of nonabelian gerbes. We also show that in phases with a dyonic condensate the low-energy theta-angle is quantized.", "doi": "10.48550/arXiv.1307.4793", "publication_date": "2013-07-17" }, { "id": "authors:tffs2-npj53", "collection": "authors", "collection_id": "tffs2-npj53", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160511-092422859", "type": "monograph", "title": "Matrix Factorizations and Kauffman Homology", "author": [ { "family_name": "Gukov", "given_name": "Sergei", "orcid": "0000-0002-9486-1762", "clpid": "Gukov-S" }, { "family_name": "Walcher", "given_name": "Johannes", "clpid": "Walcher-J" } ], "abstract": "The topological string interpretation of homological knot invariants has led to several insights into the structure of the theory in the case of sl(N). We study possible extensions of the matrix factorization approach to knot homology for other Lie groups and representations. In particular, we introduce a new triply graded theory categorifying the Kauffman polynomial, test it, and predict the Kauffman homology for several simple knots.", "doi": "10.48550/arXiv.0512298", "publication_date": "2005-12-22" }, { "id": "authors:hd8vz-wmw82", "collection": "authors", "collection_id": "hd8vz-wmw82", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160505-105657599", "type": "monograph", "title": "An Index for 2D field theories with large N=4 superconformal symmetry", "author": [ { "family_name": "Gukov", "given_name": "Sergei", "orcid": "0000-0002-9486-1762", "clpid": "Gukov-S" }, { "family_name": "Martinec", "given_name": "Emil", "clpid": "Martinec-E" }, { "family_name": "Moore", "given_name": "Gregory", "clpid": "Moore-G" }, { "family_name": "Strominger", "given_name": "Andrew", "clpid": "Strominger-A" } ], "abstract": "We consider families of theories with large N=4 superconformal symmetry. We define an index generalizing the elliptic genus of theories with N=2 symmetry. In contrast to the N=2 case, the new index constrains part of the non-BPS spectrum. Motivated by aspects of the AdS/CFT correspondence we study the index in the examples of symmetric product theories. We give a physical interpretation of the Hecke operators which appear in the expressions for partition functions of such theories. Finally, we compute the index for a nontrivial example of a symmetric product theory.", "doi": "10.48550/arXiv.0404023", "publication_date": "2004-04-02" }, { "id": "authors:6wa97-6gp76", "collection": "authors", "collection_id": "6wa97-6gp76", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160506-145809044", "type": "monograph", "title": "Chern-Simons Gauge Theory and the AdS_3/CFT_2 Correspondence", "author": [ { "family_name": "Gukov", "given_name": "Sergei", "orcid": "0000-0002-9486-1762", "clpid": "Gukov-S" }, { "family_name": "Martinec", "given_name": "Emil", "clpid": "Martinec-E" }, { "family_name": "Moore", "given_name": "Gregory", "clpid": "Moore-G" }, { "family_name": "Strominger", "given_name": "Andrew", "clpid": "Strominger-A" } ], "abstract": "The bulk partition function of pure Chern-Simons theory on a three-manifold is a state in the space of conformal blocks of the dual boundary RCFT, and therefore transforms\nnon-trivially under the boundary modular group. In contrast the bulk partition function of AdS_3 string theory is the modular-invariant partition function of the dual CFT on the\nboundary. This is a puzzle because AdS_3 string theory formally reduces to pure Chern-Simons theory at long distances. We study this puzzle in the context of massive Chern-Simons theory. We show that the puzzle is resolved in this context by the appearance of a chiral \"spectator boson\" in the boundary CFT which restores modular invariance. It couples to the conformal metric but not to the gauge field on the boundary. Consequently, we find a generalization of the standard Chern-Simons/RCFT correspondence involving \"nonholomorphic conformal blocks\" and nonrational boundary CFTs. These generalizations\nappear in the long-distance limit of AdS_3 string theory, where the role of the spectator boson is played by other degrees of freedom in the theory.", "doi": "10.48550/arXiv.0403225", "publication_date": "2004-03-22" } ]