We propose a new fermionic sum formula for the Macdonald index of a class of Argyres-Douglas theories. The formula arises naturally from a three-dimensional topological field theory obtained via a twisted dimensional reduction of the 4d theory. Such a reduction often gives rise to a 3d abelian Chern-Simons matter theory, which is expected to flow to an superconformal fixed point. After performing a topological twist, we obtain a 3d TFT admitting boundary conditions that support the vertex operator algebra associated with the original 4d theory. In this framework, the Macdonald index appears as a half-index of the 3d gauge theory, with the Macdonald grading determined by a distinguished U(1)A symmetry in the infrared superconformal algebra. We present a general procedure to identify this U(1)A symmetry and, whenever possible, show that it reproduces the refined character of the associated vertex operator algebra, thereby recovering the Macdonald index. Our construction also gives a hint towards the IR formula for the Macdonald index in terms of 4d BPS particles on the Coulomb branch.
", "doi": "10.1007/jhep03(2026)213", "issn": "1029-8479", "publisher": "Springer Science and Business Media LLC", "publication": "Journal of High Energy Physics", "publication_date": "2026-03-23", "series_number": "3", "volume": "2026", "issue": "3", "pages": "213" }, { "id": "authors:dj6rq-m5j85", "collection": "authors", "collection_id": "dj6rq-m5j85", "cite_using_url": "https://authors.library.caltech.edu/records/dj6rq-m5j85", "type": "article", "title": "Emergent \ud835\udca9=4 Supersymmetry from \ud835\udca9=1", "author": [ { "family_name": "Kang", "given_name": "Monica Jinwoo", "orcid": "0000-0002-0454-2064", "clpid": "Kang-Monica-Jinwoo" }, { "family_name": "Lawrie", "given_name": "Craig", "orcid": "0000-0002-8061-0751", "clpid": "Lawrie-Craig" }, { "family_name": "Lee", "given_name": "Ki-Hong", "orcid": "0000-0003-0069-0980", "clpid": "Lee-Ki-Hong" }, { "family_name": "Song", "given_name": "Jaewon", "orcid": "0000-0002-1238-2435", "clpid": "Song-Jaewon" } ], "abstract": "We discover a four-dimensional \ud835\udca9=1 supersymmetric field theory that is dual to the \ud835\udca9=4 super Yang-Mills theory with gauge group SU\u2062(2\u2062\ud835\udc5b+1) for each \ud835\udc5b. The dual theory is constructed through the diagonal gauging of the SU\u2062(2\u2062\ud835\udc5b+1) flavor symmetry of three copies of a strongly coupled superconformal field theory (SCFT) of Argyres-Douglas type. We find that this theory flows in the infrared to a strongly coupled \ud835\udca9=1 SCFT that lies on the same conformal manifold as \ud835\udca9=4 super Yang-Mills with gauge group SU\u2062(2\u2062\ud835\udc5b+1). Our construction provides a hint on why certain \ud835\udca9=1, 2 SCFTs have identical central charges (\ud835\udc4e=\ud835\udc50).
", "doi": "10.1103/physrevlett.130.231601", "issn": "0031-9007", "publisher": "American Physical Society", "publication": "Physical Review Letters", "publication_date": "2023-06-09", "series_number": "23", "volume": "130", "issue": "23", "pages": "231601" }, { "id": "authors:xtnex-2pk47", "collection": "authors", "collection_id": "xtnex-2pk47", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20230613-155503171", "type": "article", "title": "Operator Spectroscopy for 4D SCFTs with a = c", "author": [ { "family_name": "Kang", "given_name": "Monica Jinwoo", "orcid": "0000-0002-0454-2064", "clpid": "Kang-Monica-Jinwoo" }, { "family_name": "Lawrie", "given_name": "Craig", "orcid": "0000-0002-8061-0751", "clpid": "Lawrie-Craig" }, { "family_name": "Lee", "given_name": "Ki-Hong", "clpid": "Lee-Ki-Hong" }, { "family_name": "Song", "given_name": "Jaewon", "orcid": "0000-0002-1238-2435", "clpid": "Song-Jaewon" } ], "abstract": "We study a rich set of four-dimensional superconformal field theories with both central charges identical: a = c. These are constructed via the diagonal N = 2 or N = 1 gauging of the flavor symmetry G of a collection of N = 2 Argyres-Douglas theories of type D\u209a(G), with or without adjoint chiral multiplets, in 2106.12579 and 2111.12092. We compute superconformal indices of some theories where the rank of G is low, performing a refined test for unitarity, and further determine the relevant and marginal operator content in detail. We find that most of these theories flow to interacting superconformal field theories with a=c in the infrared.", "doi": "10.1103/PhysRevD.107.066018", "issn": "2470-0029", "publisher": "American Physical Society", "publication": "Physical Review D", "publication_date": "2023-03-15", "series_number": "6", "volume": "107", "issue": "6", "pages": "Art. No. 066018" }, { "id": "authors:c0a1a-0pt50", "collection": "authors", "collection_id": "c0a1a-0pt50", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20230328-705664700.16", "type": "article", "title": "Higgs branch, Coulomb branch, and Hall-Littlewood index", "author": [ { "family_name": "Kang", "given_name": "Monica Jinwoo", "orcid": "0000-0002-0454-2064", "clpid": "Kang-Monica-Jinwoo" }, { "family_name": "Lawrie", "given_name": "Craig", "orcid": "0000-0002-8061-0751", "clpid": "Lawrie-Craig" }, { "family_name": "Lee", "given_name": "Ki-Hong", "clpid": "Lee-Ki-Hong" }, { "family_name": "Sacchi", "given_name": "Matteo", "orcid": "0000-0003-0316-3369", "clpid": "Sacchi-Matteo" }, { "family_name": "Song", "given_name": "Jaewon", "orcid": "0000-0002-1238-2435", "clpid": "Song-Jaewon" } ], "abstract": "The Higgs branch of 4D N = 2 superconformal field theories can be analyzed via the Hilbert series of the Higgs branch or, in special cases, by computing the Hall-Littlewood index. For any class S theory corresponding to a genus-zero Riemann surface, they are conjectured to be identical. We present several families of counterexamples. We find that for any class S theory with four or more \u2124\u2082-twisted punctures, they do not match. We construct 3D mirrors for such theories and analyze their Coulomb branch Hilbert series to compute the Higgs branch Hilbert series of the 4D theory. We further construct a = c theories in class S using the twisted punctures, and these theories, which includes the D\u0302\u2084(SU(2n + 1)) theories, have Hall-Littlewood index different from the Hilbert series of the Higgs branch. We conjecture that this is the case for all a = c theories with nonempty Higgs branch, including N \u2265 3 superconformal field theories.", "doi": "10.1103/physrevd.106.106021", "issn": "2470-0010", "publisher": "American Physical Society", "publication": "Physical Review D", "publication_date": "2022-11-15", "series_number": "10", "volume": "106", "issue": "10", "pages": "Art. No. 106021" }, { "id": "authors:6480p-dxr54", "collection": "authors", "collection_id": "6480p-dxr54", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20211206-191507884", "type": "article", "title": "Infinitely many 4D N = 1 SCFTs with a = c", "author": [ { "family_name": "Kang", "given_name": "Monica Jinwoo", "orcid": "0000-0002-0454-2064", "clpid": "Kang-Monica-Jinwoo" }, { "family_name": "Lawrie", "given_name": "Craig", "orcid": "0000-0002-8061-0751", "clpid": "Lawrie-Craig" }, { "family_name": "Lee", "given_name": "Ki-Hong", "clpid": "Lee-Ki-Hong" }, { "family_name": "Song", "given_name": "Jaewon", "orcid": "0000-0002-1238-2435", "clpid": "Song-Jaewon" } ], "abstract": "We study a rich set of four-dimensional N=1 superconformal field theories (SCFTs) with both central charges identical: a=c. We construct them via the diagonal N=1 gauging of the flavor symmetry G of a collection of N=2 Argyres\u2013Douglas theories of type D_p(G), with or without additional adjoint chiral multiplets. In this way, we construct infinitely many theories that flow to interacting SCFTs with a=c in the infrared. Finally, we briefly highlight the features of the SCFTs without a=c that arise from generalizing this construction.", "doi": "10.1103/PhysRevD.105.126006", "issn": "2470-0010", "publisher": "American Physical Society", "publication": "Physical Review D", "publication_date": "2022-06-15", "series_number": "12", "volume": "105", "issue": "12", "pages": "Art. No. 126006" }, { "id": "authors:kqvrj-eva80", "collection": "authors", "collection_id": "kqvrj-eva80", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210720-225934652", "type": "article", "title": "Infinitely many 4D N = 2 SCFTs with a = c and beyond", "author": [ { "family_name": "Kang", "given_name": "Monica Jinwoo", "orcid": "0000-0002-0454-2064", "clpid": "Kang-Monica-Jinwoo" }, { "family_name": "Lawrie", "given_name": "Craig", "orcid": "0000-0002-8061-0751", "clpid": "Lawrie-Craig" }, { "family_name": "Song", "given_name": "Jaewon", "orcid": "0000-0002-1238-2435", "clpid": "Song-Jaewon" } ], "abstract": "We study a set of four-dimensional N=2 superconformal field theories (SCFTs) ^\u0393(G) labeled by a pair of simply laced Lie groups \u0393 and G. They are constructed out of gauging a number of D_p(G) and (G,G) conformal matter SCFTs; therefore, they do not have Lagrangian descriptions in general. For \u0393=D\u2084,E\u2086,E\u2087,E\u2088, and some special choices of G, the resulting theories have identical central charges (a=c) without taking any large N limit. Moreover, we find that the Schur indices for such theories can be written in terms of that of N=4 super-Yang-Mills theory upon rescaling fugacities. Especially, we find that the Schur index of ^D\u2084(SU(N)) theory for N odd is written in terms of MacMahon's generalized sum-of-divisor function, which is quasimodular. For generic choices of \u0393 and G, it can be regarded as a generalization of the affine quiver gauge theory obtained from D3-branes probing singularity of type \u0393. We also comment on a tantalizing connection regarding the theories labeled by \u0393 in the Deligne-Cvitanovi\u0107 exceptional series.", "doi": "10.1103/PhysRevD.104.105005", "issn": "2470-0010", "publisher": "American Physical Society", "publication": "Physical Review D", "publication_date": "2021-11-15", "series_number": "10", "volume": "104", "issue": "10", "pages": "Art. No. 105005" }, { "id": "authors:82p5p-hcq38", "collection": "authors", "collection_id": "82p5p-hcq38", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180712-134659218", "type": "article", "title": "Four-dimensional lens space index from two-dimensional chiral algebra", "author": [ { "family_name": "Fluder", "given_name": "Martin", "orcid": "0000-0002-0780-8550", "clpid": "Fluder-Martin" }, { "family_name": "Song", "given_name": "Jaewon", "orcid": "0000-0002-1238-2435", "clpid": "Song-Jaewon" } ], "abstract": "We study the supersymmetric partition function on S^1 \u00d7 L(r, 1), or the lens space index of four-dimensional N=2 superconformal field theories and their connection to two-dimensional chiral algebras. We primarily focus on free theories as well as ArgyresDouglas theories of type (A_1, A_k) and (A_1, D_k). We observe that in specific limits, the lens space index is reproduced in terms of the (refined) character of an appropriately twisted module of the associated two-dimensional chiral algebra or a generalized vertex operator algebra. The particular twisted module is determined by the choice of discrete holonomies for the flavor symmetry in four-dimensions.", "doi": "10.1007/JHEP07(2018)073", "issn": "1126-6708", "publisher": "Springer", "publication": "Journal of High Energy Physics", "publication_date": "2018-07", "series_number": "7", "volume": "2018", "issue": "7", "pages": "Art. No. 73" }, { "id": "authors:6rq8f-4st60", "collection": "authors", "collection_id": "6rq8f-4st60", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171113-135614634", "type": "article", "title": "Superconformal index, BPS monodromy and chiral algebras", "author": [ { "family_name": "Cecotti", "given_name": "Sergio", "clpid": "Cecotti-S" }, { "family_name": "Song", "given_name": "Jaewon", "orcid": "0000-0002-1238-2435", "clpid": "Song-Jaewon" }, { "family_name": "Vafa", "given_name": "Cumrun", "clpid": "Vafa-C" }, { "family_name": "Yan", "given_name": "Wenbin", "clpid": "Yan-Wenbin" } ], "abstract": "We show that specializations of the 4d N=2 superconformal index labeled by an integer N is given by Tr \u2133^N where \u2133 is the Kontsevich-Soibelman monodromy operator for BPS states on the Coulomb branch. We provide evidence that the states enumerated by these limits of the index lead to a family of 2d chiral algebras ANAN. This generalizes the recent results for the N = \u22121 case which corresponds to the Schur limit of the superconformal index. We show that this specialization of the index leads to the same integrand as that of the elliptic genus of compactification of the superconformal theory on S^2\u00d7 T^2 where we turn on 1/2N units of U(1)_r flux on S^2.", "doi": "10.1007/JHEP11(2017)013", "issn": "1029-8479", "publisher": "Springer", "publication": "Journal of High Energy Physics", "publication_date": "2017-11", "series_number": "11", "volume": "2017", "issue": "11", "pages": "Art. No. 013" }, { "id": "authors:x65v6-48p11", "collection": "authors", "collection_id": "x65v6-48p11", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150814-085357185", "type": "article", "title": "(0,4) dualities", "author": [ { "family_name": "Putrov", "given_name": "Pavel", "clpid": "Putrov-P" }, { "family_name": "Song", "given_name": "Jaewon", "orcid": "0000-0002-1238-2435", "clpid": "Song-Jaewon" }, { "family_name": "Yan", "given_name": "Wenbin", "clpid": "Yan-Wenbin" } ], "abstract": "We study a class of two-dimensional N=(0,4) quiver gauge theories that flow to superconformal field theories. We find dualities for the superconformal field theories similar to the 4d N=2 theories of class S, labelled by a Riemann surface C. The dual descriptions arise from various pair-of-pants decompositions, that involve an analog of the T_N theory. Especially, we find the superconformal indices of such theories can be written in terms of a topological field theory on C. We interpret this class of SCFTs as the ones coming from compactifying 6d N=(2,0) theory on CP^1\u00d7C. Moreover, some new dualities of (0,2) and (2,2) theories are also discussed.", "doi": "10.1007/JHEP03(2016)185", "issn": "1126-6708", "publisher": "Springer", "publication": "Journal of High Energy Physics", "publication_date": "2015-03-29", "series_number": "3", "volume": "2016", "issue": "3", "pages": "Art. No. 185" }, { "id": "authors:yyfkv-bq475", "collection": "authors", "collection_id": "yyfkv-bq475", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20140923-141557455", "type": "article", "title": "Quiver Tails and N=1 SCFTs from M5-branes", "author": [ { "family_name": "Agarwal", "given_name": "Prarit", "clpid": "Agarwal-P" }, { "family_name": "Bah", "given_name": "Ibrahima", "clpid": "Bah-Ibrahima" }, { "family_name": "Maruyoshi", "given_name": "Kazunobu", "clpid": "Maruyoshi-Kazunobu" }, { "family_name": "Song", "given_name": "Jaewon", "orcid": "0000-0002-1238-2435", "clpid": "Song-Jaewon" } ], "abstract": "We study a class of four-dimensional N=1 superconformal field theories obtained by wrapping M5-branes on a Riemann surface with punctures. We identify four-dimensional UV descriptions of the SCFTs corresponding to curves with a class of punctures. The quiver tails appearing in these UV descriptions differ significantly from their N=2 counterpart. We find a new type of object that we call the 'Fan'. We show how to construct new N=1 superconformal theories using the Fan. Various dual descriptions for these SCFTs can be identified with different colored pair-of-pants decompositions. For example, we find an N=1 analog of Argyres-Seiberg duality for the SU(N) SQCD with 2N flavors. We also compute anomaly coefficients and superconformal indices for these theories and show that they are invariant under dualities.", "doi": "10.1007/JHEP03(2015)049", "issn": "1126-6708", "publisher": "Springer", "publication": "Journal of High Energy Physics", "publication_date": "2015-03-10", "series_number": "3", "volume": "2015", "issue": "3", "pages": "Art. No. 049" }, { "id": "authors:s4278-jqx96", "collection": "authors", "collection_id": "s4278-jqx96", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20121012-131515139", "type": "article", "title": "Counting exceptional instantons", "author": [ { "family_name": "Keller", "given_name": "Christoph A.", "orcid": "0000-0003-2592-2012", "clpid": "Keller-C-A" }, { "family_name": "Song", "given_name": "Jaewon", "clpid": "Song-Jaewon" } ], "abstract": "We show how to obtain the instanton partition function of N = 2 SYM\nwith exceptional gauge group EFG using blow-up recursion relations derived by Nakajima\nand Yoshioka. We compute the two instanton contribution and match it with the recent\nproposal for the superconformal index of rank 2 SCFTs with E_(6,7) global symmetry.", "doi": "10.1007/JHEP07(2012)085", "issn": "1126-6708", "publisher": "Springer", "publication": "Journal of High Energy Physics", "publication_date": "2012-07-13", "series_number": "7", "volume": "2012", "issue": "7", "pages": "Art. No. 085" }, { "id": "authors:2h68t-7pw36", "collection": "authors", "collection_id": "2h68t-7pw36", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120530-093710846", "type": "article", "title": "The ABCDEFG of instantons and W-algebras", "author": [ { "family_name": "Keller", "given_name": "Christoph A.", "orcid": "0000-0003-2592-2012", "clpid": "Keller-C-A" }, { "family_name": "Mekareeya", "given_name": "Noppadol", "clpid": "Mekareeya-Noppadol" }, { "family_name": "Song", "given_name": "Jaewon", "orcid": "0000-0002-1238-2435", "clpid": "Song-Jaewon" }, { "family_name": "Tachikawa", "given_name": "Yuji", "clpid": "Tachikawa-Yuji" } ], "abstract": "For arbitrary gauge groups, we check at the one-instanton level that the Nekrasov partition function of pure N = 2 super Yang-Mills is equal to the norm of a certain coherent state of the corresponding W-algebra. For non-simply-laced gauge groups, we confirm in particular that the coherent state is in the twisted sector of a simply-laced W-algebra.", "doi": "10.1007/JHEP03(2012)045", "issn": "1126-6708", "publisher": "Springer", "publication": "Journal of High Energy Physics", "publication_date": "2012-03", "series_number": "3", "volume": "2012", "issue": "3", "pages": "Art. No. 45" }, { "id": "authors:3mbnf-s5t24", "collection": "authors", "collection_id": "3mbnf-s5t24", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120106-081215638", "type": "article", "title": "Towards a 4d/2d correspondence for Sicilian quivers", "author": [ { "family_name": "Hollands", "given_name": "Lotte", "clpid": "Hollands-Lotte" }, { "family_name": "Keller", "given_name": "Christoph A.", "orcid": "0000-0003-2592-2012", "clpid": "Keller-C-A" }, { "family_name": "Song", "given_name": "Jaewon", "orcid": "0000-0002-1238-2435", "clpid": "Song-Jaewon" } ], "abstract": "We study the 4d/2d AGT correspondence between four-dimensional instanton counting and two-dimensional conformal blocks for generalized SU(2) quiver gauge theories coming from punctured Gaiotto curves of arbitrary genus. We propose a conformal block description that corresponds to the elementary SU(2) trifundamental half-hypermultiplet, and check it against Sp(1)\u2009\u2212\u2009SO(4) instanton counting.", "doi": "10.1007/JHEP10(2011)100", "issn": "1126-6708", "publisher": "Springer", "publication": "Journal of High Energy Physics", "publication_date": "2011-10", "series_number": "10", "volume": "2011", "issue": "10", "pages": "Art. No. 100" }, { "id": "authors:y56a8-fa983", "collection": "authors", "collection_id": "y56a8-fa983", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110509-101428079", "type": "article", "title": "From SO/Sp instantons to W-algebra blocks", "author": [ { "family_name": "Hollands", "given_name": "Lotte", "clpid": "Hollands-Lotte" }, { "family_name": "Keller", "given_name": "Christoph A.", "orcid": "0000-0003-2592-2012", "clpid": "Keller-C-A" }, { "family_name": "Song", "given_name": "Jaewon", "orcid": "0000-0002-1238-2435", "clpid": "Song-Jaewon" } ], "abstract": "We study instanton partition functions for N = 2 superconformal Sp(1) and SO(4) gauge theories. We find that they agree with the corresponding U(2) instanton partitions functions only after a non-trivial mapping of the microscopic gauge couplings, since the instanton counting involves different renormalization schemes. Geometrically,\nthis mapping relates the Gaiotto curves of the different realizations as double coverings. We then formulate an AGT-type correspondence between Sp(1)/SO(4) instanton partition functions and chiral blocks with an underlying W(2, 2)-algebra symmetry. This form of the correspondence eliminates the need to divide out extra U(1) factors. Finally, to check this correspondence for linear quivers, we compute expressions for the Sp(1)\u00d7SO(4) half-bifundamental.", "doi": "10.1007/JHEP03(2011)053", "issn": "1126-6708", "publisher": "Springer", "publication": "Journal of High Energy Physics", "publication_date": "2011-03-10", "series_number": "3", "volume": "2011", "issue": "3", "pages": "Art. No. 53" }, { "id": "authors:rcb35-nzt27", "collection": "authors", "collection_id": "rcb35-nzt27", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20090729-131532827", "type": "article", "title": "Superconformal indices for orbifold Chern-Simons theories", "author": [ { "family_name": "Choi", "given_name": "Jaehyung", "clpid": "Choi-Jaehyung" }, { "family_name": "Lee", "given_name": "Sangmin", "clpid": "Lee-Sangmin" }, { "family_name": "Song", "given_name": "Jaewon", "orcid": "0000-0002-1238-2435", "clpid": "Song-Jaewon" } ], "abstract": "We calculate the superconformal indices of recently discovered three-dimensional N = 4,5 Chern-Simons-matter theories and compare them with the corresponding indices of supergravity on AdS4 times orbifolds of S^7 in the large N and large k limit. We find perfect agreement for orbifolds without fixed locus, and argue that the agreement can continue to hold for orbifolds with fixed locus provided that the mass shifts of the twisted sector states are properly taken into account. We also discuss the index for the so-called \"dual ABJM\" proposal.", "doi": "10.1088/1126-6708/2009/03/099", "issn": "1126-6708", "publisher": "Springer", "publication": "Journal of High Energy Physics", "publication_date": "2009-03-17", "series_number": "3", "volume": "2009", "issue": "3", "pages": "099" }, { "id": "authors:7my47-98y11", "collection": "authors", "collection_id": "7my47-98y11", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20090817-101240132", "type": "article", "title": "Current correlators for general gauge mediation", "author": [ { "family_name": "Ooguri", "given_name": "Hirosi", "orcid": "0000-0001-6021-3778", "clpid": "Ooguri-H" }, { "family_name": "Ookouchi", "given_name": "Yutaka", "clpid": "Ookouchi-Yutaka" }, { "family_name": "Park", "given_name": "Chang-Soon", "clpid": "Park-Chang-Soon" }, { "family_name": "Song", "given_name": "Jaewon", "orcid": "0000-0002-1238-2435", "clpid": "Song-Jaewon" } ], "abstract": "In the gauge mediation mechanism, the effects of the hidden sector are characterized by a set of correlation functions of the global symmetry current of the hidden sector. We present methods to compute these correlators in cases with strongly coupled hidden sectors. Several examples are presented to demonstrate the technique explicitly.", "doi": "10.1016/j.nuclphysb.2008.09.017", "issn": "0550-3213", "publisher": "Elsevier", "publication": "Nuclear Physics B", "publication_date": "2009-02-11", "series_number": "1-2", "volume": "808", "issue": "1-2", "pages": "121-136" } ]