Abstract
We study the cohomology of local BPS operators in \( \mathcal{N} \) = 4 Yang-Mills theory. The finite N cohomologies consist of the graviton part (subject to the stringy exclusion principle) and the rest which may describe black hole microstates in quantum AdS/CFT. We construct an infinite tower of non-graviton cohomologies in the SU(2) theory and study to what extent they simulate quantum black holes. We find signals for partial no-hair behaviors by showing that certain gravitons are forbidden to dress these cohomologies. This is in qualitative agreement with the perturbative hairs allowed around black holes, which also leads us to a natural setup to construct hairy BPS black holes. The cohomologies are simpler to study in the BMN matrix model truncation of the classical field theory.
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References
J.D. Bekenstein, Black holes and entropy, Phys. Rev. D 7 (1973) 2333 [INSPIRE].
S.W. Hawking, Particle Creation by Black Holes, Commun. Math. Phys. 43 (1975) 199 [Erratum ibid. 46 (1976) 206] [INSPIRE].
J.D. Bekenstein, A Universal Upper Bound on the Entropy to Energy Ratio for Bounded Systems, Phys. Rev. D 23 (1981) 287 [INSPIRE].
E. Witten, Anti-de Sitter space, thermal phase transition, and confinement in gauge theories, Adv. Theor. Math. Phys. 2 (1998) 505 [hep-th/9803131] [INSPIRE].
B. Sundborg, The Hagedorn transition, deconfinement and N=4 SYM theory, Nucl. Phys. B 573 (2000) 349 [hep-th/9908001] [INSPIRE].
O. Aharony et al., The Hagedorn - deconfinement phase transition in weakly coupled large N gauge theories, Adv. Theor. Math. Phys. 8 (2004) 603 [hep-th/0310285] [INSPIRE].
J.M. Maldacena, The large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [hep-th/9711200] [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].
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. 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].
R.A. Janik and M. Trzetrzelewski, Supergravitons from one loop perturbative N=4 SYM, Phys. Rev. D 77 (2008) 085024 [arXiv:0712.2714] [INSPIRE].
L. Grant, P.A. Grassi, S. Kim and S. Minwalla, Comments on 1/16 BPS Quantum States and Classical Configurations, JHEP 05 (2008) 049 [arXiv:0803.4183] [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].
S. Minwalla, Supersymmetric States in \( \mathcal{N} \) = 4 Yang Mills, talk given at Strings 2006, Beijing.
C.-M. Chang and Y.-H. Lin, Words to describe a black hole, JHEP 02 (2023) 109 [arXiv:2209.06728] [INSPIRE].
J. McGreevy, L. Susskind and N. Toumbas, Invasion of the giant gravitons from Anti-de Sitter space, JHEP 06 (2000) 008 [hep-th/0003075] [INSPIRE].
M.T. Grisaru, R.C. Myers and O. Tafjord, SUSY and goliath, JHEP 08 (2000) 040 [hep-th/0008015] [INSPIRE].
A. Hashimoto, S. Hirano and N. Itzhaki, Large branes in AdS and their field theory dual, JHEP 08 (2000) 051 [hep-th/0008016] [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].
M. Honda, Quantum Black Hole Entropy from 4d Supersymmetric Cardy formula, Phys. Rev. D 100 (2019) 026008 [arXiv:1901.08091] [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].
S. Choi, S. Kim, E. Lee and J. Park, The shape of non-graviton operators for SU(2), arXiv:2209.12696 [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].
N. Kim, T. Klose and J. Plefka, Plane wave matrix theory from N=4 superYang-Mills on R x S**3, Nucl. Phys. B 671 (2003) 359 [hep-th/0306054] [INSPIRE].
P. Basu et al., Small Hairy Black Holes in Global AdS Spacetime, JHEP 10 (2010) 045 [arXiv:1003.3232] [INSPIRE].
S. Bhattacharyya, S. Minwalla and K. Papadodimas, Small Hairy Black Holes in AdS5xS5, JHEP 11 (2011) 035 [arXiv:1005.1287] [INSPIRE].
J. Markeviciute and J.E. Santos, Evidence for the existence of a novel class of supersymmetric black holes with AdS5 × S5 asymptotics, Class. Quant. Grav. 36 (2019) 02LT01 [arXiv:1806.01849] [INSPIRE].
J. Markeviciute, Rotating Hairy Black Holes in AdS5 × S5, JHEP 03 (2019) 110 [arXiv:1809.04084] [INSPIRE].
Monte Carlo String/M-theory (MCSMC) collaboration, Precision test of gauge/gravity duality in D0-brane matrix model at low temperature, JHEP 03 (2023) 071 [arXiv:2210.04881] [INSPIRE].
A. Biggs and J. Maldacena, Scaling similarities and quasinormal modes of D0 black hole solutions, arXiv:2303.09974 [INSPIRE].
J. Maldacena, A simple quantum system that describes a black hole, arXiv:2303.11534 [INSPIRE].
N. Beisert, The dilatation operator of N=4 super Yang-Mills theory and integrability, Phys. Rept. 405 (2004) 1 [hep-th/0407277] [INSPIRE].
C. Cordova, T.T. Dumitrescu and K. Intriligator, Multiplets of Superconformal Symmetry in Diverse Dimensions, JHEP 03 (2019) 163 [arXiv:1612.00809] [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].
S. Choi, S. Kim, E. Lee and J. Lee, From giant gravitons to black holes, arXiv:2207.05172 [INSPIRE].
I. Biswas, D. Gaiotto, S. Lahiri and S. Minwalla, Supersymmetric states of N=4 Yang-Mills from giant gravitons, JHEP 12 (2007) 006 [hep-th/0606087] [INSPIRE].
G. Mandal and N.V. Suryanarayana, Counting 1/8-BPS dual-giants, JHEP 03 (2007) 031 [hep-th/0606088] [INSPIRE].
J.M. Maldacena, M.M. Sheikh-Jabbari and M. Van Raamsdonk, Transverse five-branes in matrix theory, JHEP 01 (2003) 038 [hep-th/0211139] [INSPIRE].
A. Hanany, N. Mekareeya and G. Torri, The Hilbert Series of Adjoint SQCD, Nucl. Phys. B 825 (2010) 52 [arXiv:0812.2315] [INSPIRE].
S. Choi, S. Jeong and S. Kim, The Yang-Mills duals of small AdS black holes, arXiv:2103.01401 [INSPIRE].
A. Dabholkar, M. Guica, S. Murthy and S. Nampuri, No entropy enigmas for N=4 dyons, JHEP 06 (2010) 007 [arXiv:0903.2481] [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].
J.T. Liu, H. Lu, C.N. Pope and J.F. Vazquez-Poritz, New supersymmetric solutions of N=2, D=5 gauged supergravity with hyperscalars, JHEP 10 (2007) 093 [arXiv:0705.2234] [INSPIRE].
J. Bellorin and T. Ortin, Characterization of all the supersymmetric solutions of gauged N=1, d=5 supergravity, JHEP 08 (2007) 096 [arXiv:0705.2567] [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].
Acknowledgments
We thank Francesco Benini, Nakwoo Kim, Seungkyu Kim, Ki-Hong Lee, Kimyeong Lee, Shiraz Minwalla, Silviu S. Pufu, Jaewon Song and Gustavo J. Turiaci for helpful discussions. This work is supported in part by a KIAS Individual Grant PG081602 at Korea Institute for Advanced Study (SC), the DoE grant DE-SC0007859 (SL) and the NRF grants 2021R1A2C2012350 (SK, EL), 2021R1A6A1A10042944 (JP), 2021R1A2C1012440 (JP).
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Choi, S., Kim, S., Lee, E. et al. Towards quantum black hole microstates. J. High Energ. Phys. 2023, 175 (2023). https://doi.org/10.1007/JHEP11(2023)175
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DOI: https://doi.org/10.1007/JHEP11(2023)175