Abstract
We show that the Bekenstein-Hawking entropy of large supersymmetric black holes in AdS5 × S5 emerges from remarkable cancellations in the giant graviton expansions recently proposed by Imamura, and Gaiotto and Lee, independently. A similar cancellation mechanism is shown to happen in the exact expansion in terms of free fermions recently put-forward by Murthy. These two representations can be understood as sums over independent systems of giant D3-branes and free fermions, respectively. At large charges, the free energy of each independent system localizes to its asymptotic expansion near the leading singularity. The sum over the independent systems maps their localized free energy to the localized free energy of the superconformal index of U(N) \(\mathcal{N}\) = 4 SYM. This result constitutes a non-perturbative test of the giant graviton expansion valid at any value of N. Moreover, in the holographic scaling limit N → ∞ at fixed ratio \(\frac{{\text{Entropy}}}{{N}^{2}}\), it recovers the 1/16 BPS black hole entropy by a saddle-point approximation of the giant graviton expansion.
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References
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].
C. Romelsberger, Counting chiral primaries in N = 1, d = 4 superconformal field theories, Nucl. Phys. B 747 (2006) 329 [hep-th/0510060] [INSPIRE].
Y. Imamura, Finite-N superconformal index via the AdS/CFT correspondence, PTEP 2021 (2021) 123B05 [arXiv:2108.12090] [INSPIRE].
R. Arai and Y. Imamura, Finite N Corrections to the Superconformal Index of S-fold Theories, PTEP 2019 (2019) 083B04 [arXiv:1904.09776] [INSPIRE].
D. Gaiotto and J.H. Lee, The Giant Graviton Expansion, arXiv:2109.02545 [INSPIRE].
J.H. Lee, Exact stringy microstates from gauge theories, JHEP 11 (2022) 137 [arXiv:2204.09286] [INSPIRE].
S. Murthy, The growth of the \(\frac{1}{16}\)-BPS index in 4d \(\mathcal{N}\) = 4 SYM, arXiv:2005.10843 [INSPIRE].
P. Agarwal et al., AdS black holes and finite N indices, Phys. Rev. D 103 (2021) 126006 [arXiv:2005.11240] [INSPIRE].
A. Cabo-Bizet, D. Cassani, D. Martelli and S. Murthy, Microscopic origin of the Bekenstein-Hawking entropy of supersymmetric AdS5 black holes, JHEP 10 (2019) 062 [arXiv:1810.11442] [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 \(\mathcal{N}\) =4 Super-Yang-Mills Field Theory, Phys. Rev. X 10 (2020) 021037 [arXiv:1812.09613] [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.T. Liu and N.J. Rajappa, Finite N indices and the giant graviton expansion, JHEP 04 (2023) 078 [arXiv:2212.05408] [INSPIRE].
D.S. Eniceicu, Comments on the Giant-Graviton Expansion of the Superconformal Index, arXiv:2302.04887 [INSPIRE].
D. Berenstein and S. Wang, BPS coherent states and localization, JHEP 08 (2022) 164 [arXiv:2203.15820] [INSPIRE].
H. Lin, Coherent state operators, giant gravitons, and gauge-gravity correspondence, Annals Phys. 451 (2023) 169248 [arXiv:2212.14002] [INSPIRE].
M. Beccaria and A. Cabo-Bizet, On the brane expansion of the Schur index, JHEP 08 (2023) 073 [arXiv:2305.17730] [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 \(\mathcal{N}\) = 4 index and AdS5 blackholes, JHEP 06 (2019) 134 [arXiv:1902.06619] [INSPIRE].
J. Kim, S. Kim and J. Song, A 4d \(\mathcal{N}\) = 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 \(\mathcal{N}\) = 1 superconformal index, JHEP 08 (2019) 120 [arXiv:1904.05865] [INSPIRE].
D. Cassani and Z. Komargodski, EFT and the SUSY Index on the 2nd Sheet, SciPost Phys. 11 (2021) 004 [arXiv:2104.01464] [INSPIRE].
S. Choi, S. Kim, E. Lee and J. Lee, From giant gravitons to black holes, JHEP 11 (2023) 086 [arXiv:2207.05172] [INSPIRE].
J.B. Gutowski and H.S. Reall, Supersymmetric AdS(5) black holes, JHEP 02 (2004) 006 [hep-th/0401042] [INSPIRE].
J.B. Gutowski and H.S. Reall, General supersymmetric AdS(5) black holes, JHEP 04 (2004) 048 [hep-th/0401129] [INSPIRE].
M. Cvetic, H. Lu and C.N. Pope, Charged rotating black holes in five dimensional U (1)3 gauged N = 2 supergravity, Phys. Rev. D 70 (2004) 081502 [hep-th/0407058] [INSPIRE].
A. Cabo-Bizet, From multi-gravitons to Black holes: The role of complex saddles, arXiv:2012.04815 [INSPIRE].
A. Cabo-Bizet and S. Murthy, Supersymmetric phases of 4d \(\mathcal{N}\) = 4 SYM at large N , JHEP 09 (2020) 184 [arXiv:1909.09597] [INSPIRE].
A. Cabo-Bizet, D. Cassani, D. Martelli and S. Murthy, The large-N limit of the 4d \(\mathcal{N}\) = 1 superconformal index, JHEP 11 (2020) 150 [arXiv:2005.10654] [INSPIRE].
O. Aharony, F. Benini, O. Mamroud and E. Milan, A gravity interpretation for the Bethe Ansatz expansion of the \(\mathcal{N}\) = 4 SYM index, Phys. Rev. D 104 (2021) 086026 [arXiv:2104.13932] [INSPIRE].
O. Mamroud, The SUSY index beyond the Cardy limit, JHEP 01 (2024) 111 [arXiv:2212.11925] [INSPIRE].
Y. Chen, M. Heydeman, Y. Wang and M. Zhang, Probing supersymmetric black holes with surface defects, JHEP 10 (2023) 136 [arXiv:2306.05463] [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].
D.E. Berenstein, J.M. Maldacena and H.S. Nastase, Strings in flat space and pp waves from N = 4 superYang-Mills, JHEP 04 (2002) 013 [hep-th/0202021] [INSPIRE].
L.F. Alday and J.M. Maldacena, Comments on operators with large spin, JHEP 11 (2007) 019 [arXiv:0708.0672] [INSPIRE].
B. Basso and G.P. Korchemsky, Anomalous dimensions of high-spin operators beyond the leading order, Nucl. Phys. B 775 (2007) 1 [hep-th/0612247] [INSPIRE].
Z. Komargodski and A. Zhiboedov, Convexity and Liberation at Large Spin, JHEP 11 (2013) 140 [arXiv:1212.4103] [INSPIRE].
A.L. Fitzpatrick, J. Kaplan, D. Poland and D. Simmons-Duffin, The Analytic Bootstrap and AdS Superhorizon Locality, JHEP 12 (2013) 004 [arXiv:1212.3616] [INSPIRE].
L.Á. Gaumé, D. Orlando and S. Reffert, Selected topics in the large quantum number expansion, Phys. Rept. 933 (2021) 1 [arXiv:2008.03308] [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].
K. Goldstein et al., Residues, modularity, and the Cardy limit of the 4d \(\mathcal{N}\) = 4 superconformal index, JHEP 04 (2021) 216 [arXiv:2011.06605] [INSPIRE].
A. Amariti, M. Fazzi and A. Segati, The SCI of \(\mathcal{N}\) = 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 \(\mathcal{N}\) = 1 ABCD SCFTs, JHEP 07 (2021) 141 [arXiv:2103.15853] [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].
V. Jejjala, Y. Lei, S. van Leuven and W. Li, SL(3, \({\mathbb{Z}}\)) Modularity and New Cardy limits of the \(\mathcal{N}\) = 4 superconformal index, JHEP 11 (2021) 047 [arXiv:2104.07030] [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. Cabo-Bizet, On the 4d superconformal index near roots of unity: bulk and localized contributions, JHEP 02 (2023) 134 [arXiv:2111.14941] [INSPIRE].
A. Cabo-Bizet, Quantum phases of 4d SU(N) \(\mathcal{N}\) = 4 SYM, JHEP 10 (2022) 052 [arXiv:2111.14942] [INSPIRE].
V. Jejjala, Y. Lei, S. van Leuven and W. Li, Modular factorization of superconformal indices, JHEP 10 (2023) 105 [arXiv:2210.17551] [INSPIRE].
A. Amariti and A. Zanetti, S-duality in the Cardy-like limit of the superconformal index, JHEP 02 (2024) 218 [arXiv:2307.08391] [INSPIRE].
S. Choi, C. Hwang and S. Kim, Quantum vortices, M2-branes and black holes, arXiv:1908.02470 [INSPIRE].
J. Nian and L.A. Pando Zayas, Microscopic entropy of rotating electrically charged AdS4 black holes from field theory localization, JHEP 03 (2020) 081 [arXiv:1909.07943] [INSPIRE].
A. González Lezcano, M. Jerdee and L.A. Pando Zayas, Cardy expansion of 3d superconformal indices and corrections to the dual black hole entropy, JHEP 01 (2023) 044 [arXiv:2210.12065] [INSPIRE].
P. Benetti Genolini, A. Cabo-Bizet and S. Murthy, Supersymmetric phases of AdS4/CFT3, JHEP 06 (2023) 125 [arXiv:2301.00763] [INSPIRE].
A. Amariti, J. Nian, L.A. Pando Zayas and A. Segati, Universal Cardy-Like Behavior of 3D A-Twisted Partition Functions, arXiv:2306.05462 [INSPIRE].
N. Bobev, V. Dimitrov, V. Reys and A. Vekemans, Higher derivative corrections and AdS5 black holes, Phys. Rev. D 106 (2022) L121903 [arXiv:2207.10671] [INSPIRE].
D. Cassani, A. Ruipérez and E. Turetta, Corrections to AdS5 black hole thermodynamics from higher-derivative supergravity, JHEP 11 (2022) 059 [arXiv:2208.01007] [INSPIRE].
D. Cassani, A. Ruipérez and E. Turetta, Boundary terms and conserved charges in higher-derivative gauged supergravity, JHEP 06 (2023) 203 [arXiv:2304.06101] [INSPIRE].
M. Berkooz, D. Reichmann and J. Simon, A Fermi Surface Model for Large Supersymmetric AdS(5) Black Holes, JHEP 01 (2007) 048 [hep-th/0604023] [INSPIRE].
M. Berkooz and D. Reichmann, Weakly Renormalized Near 1/16 SUSY Fermi Liquid Operators in N = 4 SYM, JHEP 10 (2008) 084 [arXiv:0807.0559] [INSPIRE].
C.-M. Chang, L. Feng, Y.-H. Lin and Y.-X. Tao, Decoding stringy near-supersymmetric black holes, arXiv:2306.04673 [INSPIRE].
K. Budzik, H. Murali and P. Vieira, Following Black Hole States, arXiv:2306.04693 [INSPIRE].
J. Caetano, S. Komatsu and Y. Wang, Large charge ’t Hooft limit of \(\mathcal{N}\) = 4 super-Yang-Mills, JHEP 02 (2024) 047 [arXiv:2306.00929] [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 \(\mathcal{N}\) = 4 SYM, arXiv:2203.01331 [INSPIRE].
G.J. Turiaci and E. Witten, \(\mathcal{N}\) = 2 JT supergravity and matrix models, JHEP 12 (2023) 003 [arXiv:2305.19438] [INSPIRE].
C.-M. Chang and X. Yin, 1/16 BPS states in \(\mathcal{N}\) = 4 super-Yang-Mills theory, Phys. Rev. D 88 (2013) 106005 [arXiv:1305.6314] [INSPIRE].
F.A. Dolan and H. Osborn, Applications of the Superconformal Index for Protected Operators and q-Hypergeometric Identities to N = 1 Dual Theories, Nucl. Phys. B 818 (2009) 137 [arXiv:0801.4947] [INSPIRE].
F. Benini and E. Milan, A Bethe Ansatz type formula for the superconformal index, Commun. Math. Phys. 376 (2020) 1413 [arXiv:1811.04107] [INSPIRE].
A. Narukawa, The modular properties and the integral representations of the multiple elliptic gamma functions, math/0306164.
G. Felder and A. Varchenko, The Elliptic Gamma Function and SL(3, Z) ⋉ Z3, Adv. Math. 156 (2000) 44.
Acknowledgments
We thank J. Caetano, S. Kim, J. H. Lee, and D. Orlando for useful conversations. We also acknowledge financial support from the INFN grant GSS (Gauge Theories, Strings and Supergravity). This work benefited from the participation of ACB in the workshops “Precision Holography” and “Exact Results and Holographic Correspondences” held at CERN and MITP, respectively. ACB would also like to thank the Isaac Newton Institute for Mathematical Sciences, Cambridge, for support and hospitality during the programme Black holes: bridges between number theory and holographic quantum information, where work on this paper was undertaken. This work was supported by EPSRC grant EP/R014604/1.
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Beccaria, M., Cabo-Bizet, A. Large black hole entropy from the giant brane expansion. J. High Energ. Phys. 2024, 146 (2024). https://doi.org/10.1007/JHEP04(2024)146
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DOI: https://doi.org/10.1007/JHEP04(2024)146