Abstract
We evaluate the superconformal index of 4d \( \mathcal{N} \) = 4 SYM with gauge algebra so(2Nc + 1) in the Cardy-like limit. We then study the relation with the results obtained for the S-dual usp(2Nc), discussing the fate of S-duality in different regions of charges. We find that S-duality is preserved thanks to a non-trivial integral identity that relates the three sphere partition functions of pure 3d Chern-Simons gauge theories.
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J.B. Gutowski and H.S. Reall, General supersymmetric AdS5 black holes, JHEP 04 (2004) 048 [hep-th/0401129] [INSPIRE].
J.B. Gutowski and H.S. Reall, Supersymmetric AdS5 black holes, JHEP 02 (2004) 006 [hep-th/0401042] [INSPIRE].
S.M. Hosseini, K. Hristov and A. Zaffaroni, An extremization principle for the entropy of rotating BPS black holes in AdS5, JHEP 07 (2017) 106 [arXiv:1705.05383] [INSPIRE].
S. Choi, J. Kim, S. Kim and J. Nahmgoong, Large AdS black holes from QFT, arXiv:1810.12067 [INSPIRE].
F. Benini and E. Milan, Black holes in 4D N = 4 super-Yang-Mills field theory, Phys. Rev. X 10 (2020) 021037 [arXiv:1812.09613] [INSPIRE].
C. Romelsberger, Counting chiral primaries in N = 1, d = 4 superconformal field theories, Nucl. Phys. B 747 (2006) 329 [hep-th/0510060] [INSPIRE].
J. Kinney, J.M. Maldacena, S. Minwalla and S. Raju, An index for 4 dimensional super conformal theories, Commun. Math. Phys. 275 (2007) 209 [hep-th/0510251] [INSPIRE].
M. Honda, Quantum black hole entropy from 4d supersymmetric Cardy formula, Phys. Rev. D 100 (2019) 026008 [arXiv:1901.08091] [INSPIRE].
A. Arabi Ardehali, Cardy-like asymptotics of the 4d N = 4 index and AdS5 blackholes, JHEP 06 (2019) 134 [arXiv:1902.06619] [INSPIRE].
J. Kim, S. Kim and J. Song, A 4d N = 1 Cardy formula, JHEP 01 (2021) 025 [arXiv:1904.03455] [INSPIRE].
A. Cabo-Bizet, D. Cassani, D. Martelli and S. Murthy, The asymptotic growth of states of the 4d N = 1 superconformal index, JHEP 08 (2019) 120 [arXiv:1904.05865] [INSPIRE].
A. Amariti, I. Garozzo and G. Lo Monaco, Entropy function from toric geometry, Nucl. Phys. B 973 (2021) 115571 [arXiv:1904.10009] [INSPIRE].
A. González Lezcano and L.A. Pando Zayas, Microstate counting via Bethe Ansätze in the 4d N = 1 superconformal index, JHEP 03 (2020) 088 [arXiv:1907.12841] [INSPIRE].
A. Lanir, A. Nedelin and O. Sela, Black hole entropy function for toric theories via Bethe Ansatz, JHEP 04 (2020) 091 [arXiv:1908.01737] [INSPIRE].
A. Cabo-Bizet and S. Murthy, Supersymmetric phases of 4d N = 4 SYM at large N, JHEP 09 (2020) 184 [arXiv:1909.09597] [INSPIRE].
A. Arabi Ardehali, J. Hong and J.T. Liu, Asymptotic growth of the 4d N = 4 index and partially deconfined phases, JHEP 07 (2020) 073 [arXiv:1912.04169] [INSPIRE].
S. Murthy, The growth of the \( \frac{1}{16} \)-BPS index in 4d N = 4 SYM, arXiv:2005.10843 [INSPIRE].
K. Goldstein et al., Residues, modularity, and the Cardy limit of the 4d N = 4 superconformal index, JHEP 04 (2021) 216 [arXiv:2011.06605] [INSPIRE].
A. Cabo-Bizet, D. Cassani, D. Martelli and S. Murthy, The large-N limit of the 4d N = 1 superconformal index, JHEP 11 (2020) 150 [arXiv:2005.10654] [INSPIRE].
P. Agarwal et al., AdS black holes and finite N indices, Phys. Rev. D 103 (2021) 126006 [arXiv:2005.11240] [INSPIRE].
F. Benini et al., Superconformal indices at large N and the entropy of AdS5 × SE5 black holes, Class. Quant. Grav. 37 (2020) 215021 [arXiv:2005.12308] [INSPIRE].
A. Cabo-Bizet, From multi-gravitons to black holes: the role of complex saddles, arXiv:2012.04815 [INSPIRE].
A. González Lezcano, J. Hong, J.T. Liu and L.A. Pando Zayas, Sub-leading structures in superconformal indices: subdominant saddles and logarithmic contributions, JHEP 01 (2021) 001 [arXiv:2007.12604] [INSPIRE].
A. Amariti, M. Fazzi and A. Segati, The SCI of N = 4 USp(2Nc) and SO(Nc) SYM as a matrix integral, JHEP 06 (2021) 132 [arXiv:2012.15208] [INSPIRE].
A. Amariti, M. Fazzi and A. Segati, Expanding on the Cardy-like limit of the SCI of 4d N = 1 ABCD SCFTs, JHEP 07 (2021) 141 [arXiv:2103.15853] [INSPIRE].
O. Aharony, F. Benini, O. Mamroud and E. Milan, A gravity interpretation for the Bethe Ansatz expansion of the N = 4 SYM index, Phys. Rev. D 104 (2021) 086026 [arXiv:2104.13932] [INSPIRE].
E. Colombo, The large-N limit of 4d superconformal indices for general BPS charges, JHEP 12 (2022) 013 [arXiv:2110.01911] [INSPIRE].
S. Choi, S. Jeong, S. Kim and E. Lee, Exact QFT duals of AdS black holes, JHEP 09 (2023) 138 [arXiv:2111.10720] [INSPIRE].
A. Cabo-Bizet, On the 4d superconformal index near roots of unity: bulk and localized contributions, JHEP 02 (2023) 134 [arXiv:2111.14941] [INSPIRE].
V. Jejjala, Y. Lei, S. van Leuven and W. Li, SL(3, Z) modularity and new Cardy limits of the N = 4 superconformal index, JHEP 11 (2021) 047 [arXiv:2104.07030] [INSPIRE].
S. Murthy, Unitary matrix models, free fermions, and the giant graviton expansion, Pure Appl. Math. Quart. 19 (2023) 299 [arXiv:2202.06897] [INSPIRE].
J. Boruch, M.T. Heydeman, L.V. Iliesiu and G.J. Turiaci, BPS and near-BPS black holes in AdS5 and their spectrum in N = 4 SYM, arXiv:2203.01331 [INSPIRE].
O. Mamroud, The SUSY index beyond the Cardy limit, JHEP 01 (2024) 111 [arXiv:2212.11925] [INSPIRE].
V. Jejjala, Y. Lei, S. van Leuven and W. Li, Modular factorization of superconformal indices, JHEP 10 (2023) 105 [arXiv:2210.17551] [INSPIRE].
D. Cassani and Z. Komargodski, EFT and the SUSY index on the 2nd sheet, SciPost Phys. 11 (2021) 004 [arXiv:2104.01464] [INSPIRE].
A. Arabi Ardehali and S. Murthy, The 4d superconformal index near roots of unity and 3d Chern-Simons theory, JHEP 10 (2021) 207 [arXiv:2104.02051] [INSPIRE].
L. Di Pietro and Z. Komargodski, Cardy formulae for SUSY theories in d = 4 and d = 6, JHEP 12 (2014) 031 [arXiv:1407.6061] [INSPIRE].
O. Aharony, S.S. Razamat, N. Seiberg and B. Willett, 3d dualities from 4d dualities, JHEP 07 (2013) 149 [arXiv:1305.3924] [INSPIRE].
A.A. Ardehali and J. Hong, Decomposition of BPS moduli spaces and asymptotics of supersymmetric partition functions, JHEP 01 (2022) 062 [arXiv:2110.01538] [INSPIRE].
A. Gadde, E. Pomoni, L. Rastelli and S.S. Razamat, S-duality and 2d topological QFT, JHEP 03 (2010) 032 [arXiv:0910.2225] [INSPIRE].
V.P. Spiridonov and G.S. Vartanov, Superconformal indices of N = 4 SYM field theories, Lett. Math. Phys. 100 (2012) 97 [arXiv:1005.4196] [INSPIRE].
A. Kapustin, B. Willett and I. Yaakov, Exact results for Wilson loops in superconformal Chern-Simons theories with matter, JHEP 03 (2010) 089 [arXiv:0909.4559] [INSPIRE].
G. Gasaneo, F.D. Colavecchia, S. Otranto and C.R. Garibotti, The hyperbolic-hypergeometric functions, J. Math. Phys. 42 (2001) 4971.
A. Amariti and M. Fazzi, Dualities for three-dimensional N = 2 SU(Nc) chiral adjoint SQCD, JHEP 11 (2020) 030 [arXiv:2007.01323] [INSPIRE].
Acknowledgments
The work of A.A., A.Z. . has been supported in part by the Italian Ministero dell’Istruzione, Università e Ricerca (MIUR), in part by Istituto Nazionale di Fisica Nucleare (INFN) through the “Gauge Theories, Strings, Supergravity” (GSS) research project and in part by MIUR-PRIN contract 2017CC72MK-003.
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Amariti, A., Zanetti, A. S-duality in the Cardy-like limit of the superconformal index. J. High Energ. Phys. 2024, 218 (2024). https://doi.org/10.1007/JHEP02(2024)218
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DOI: https://doi.org/10.1007/JHEP02(2024)218