Abstract
The gravitational path integral can be used to compute the number of black hole states for a given energy window, or the free energy in a thermal ensemble. In this article we explain how to use the gravitational path integral to compute the separate number of bosonic and fermionic black hole microstates. We do this by comparing the partition function with and without the insertion of (−1)F. In particular we introduce a universal rotating black hole that contributes to the partition function in the presence of (−1)F. We study this problem for black holes in asymptotically flat space and in AdS, putting constraints on the high energy spectrum of holographic CFTs (not necessarily supersymmetric). Finally, we analyze wormhole contributions to related quantities.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
G.W. Gibbons and S.W. Hawking, Action Integrals and Partition Functions in Quantum Gravity, Phys. Rev. D 15 (1977) 2752 [INSPIRE].
A. Cherman, M. Shifman and M. Ünsal, Bose-Fermi cancellations without supersymmetry, Phys. Rev. D 99 (2019) 105001 [arXiv:1812.04642] [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].
N. Bobev, A.M. Charles and V.S. Min, Euclidean black saddles and AdS4 black holes, JHEP 10 (2020) 073 [arXiv:2006.01148] [INSPIRE].
L.V. Iliesiu, M. Kologlu and G.J. Turiaci, Supersymmetric indices factorize, JHEP 05 (2023) 032 [arXiv:2107.09062] [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].
J.S. Cotler et al., Black Holes and Random Matrices, JHEP 05 (2017) 118 [Erratum ibid. 09 (2018) 002] [arXiv:1611.04650] [INSPIRE].
P. Saad, S.H. Shenker and D. Stanford, A semiclassical ramp in SYK and in gravity, arXiv:1806.06840 [INSPIRE].
S. Pal and Z. Sun, High Energy Modular Bootstrap, Global Symmetries and Defects, JHEP 08 (2020) 064 [arXiv:2004.12557] [INSPIRE].
D. Harlow and H. Ooguri, A universal formula for the density of states in theories with finite-group symmetry, Class. Quant. Grav. 39 (2022) 134003 [arXiv:2109.03838] [INSPIRE].
B. Mukhametzhanov and S. Pal, Beurling-Selberg Extremization and Modular Bootstrap at High Energies, SciPost Phys. 8 (2020) 088 [arXiv:2003.14316] [INSPIRE].
S. Pal, J. Qiao and S. Rychkov, Twist Accumulation in Conformal Field Theory: A Rigorous Approach to the Lightcone Bootstrap, Commun. Math. Phys. 402 (2023) 2169 [arXiv:2212.04893] [INSPIRE].
S. Pal and J. Qiao, Lightcone Modular Bootstrap and Tauberian Theory: A Cardy-like Formula for Near-extremal Black Holes, arXiv:2307.02587 [INSPIRE].
E. Witten, Constraints on Supersymmetry Breaking, Nucl. Phys. B 202 (1982) 253 [INSPIRE].
A.A. H., P.V. Athira, C. Chowdhury and A. Sen, Logarithmic correction to BPS black hole entropy from supersymmetric index at finite temperature, JHEP 03 (2024) 095 [arXiv:2306.07322] [INSPIRE].
E. Witten, A Note On Complex Spacetime Metrics, arXiv:2111.06514 [INSPIRE].
A. Ghosh, H. Maxfield and G.J. Turiaci, A universal Schwarzian sector in two-dimensional conformal field theories, JHEP 05 (2020) 104 [arXiv:1912.07654] [INSPIRE].
L.V. Iliesiu and G.J. Turiaci, The statistical mechanics of near-extremal black holes, JHEP 05 (2021) 145 [arXiv:2003.02860] [INSPIRE].
M. Heydeman, L.V. Iliesiu, G.J. Turiaci and W. Zhao, The statistical mechanics of near-BPS black holes, J. Phys. A 55 (2022) 014004 [arXiv:2011.01953] [INSPIRE].
G.J. Turiaci, New insights on near-extremal black holes, arXiv:2307.10423 [INSPIRE].
A. Chamblin, R. Emparan, C.V. Johnson and R.C. Myers, Charged AdS black holes and catastrophic holography, Phys. Rev. D 60 (1999) 064018 [hep-th/9902170] [INSPIRE].
M. Kontsevich and G. Segal, Wick Rotation and the Positivity of Energy in Quantum Field Theory, Quart. J. Math. Oxford Ser. 72 (2021) 673 [arXiv:2105.10161] [INSPIRE].
J.M. Maldacena and A. Strominger, AdS(3) black holes and a stringy exclusion principle, JHEP 12 (1998) 005 [hep-th/9804085] [INSPIRE].
A. Maloney and E. Witten, Quantum Gravity Partition Functions in Three Dimensions, JHEP 02 (2010) 029 [arXiv:0712.0155] [INSPIRE].
D. Harlow, Gauging spacetime inversions, Talk at ExU-YITP Workshop on Holography, Gravity and Quantum Information, (2023), https://www2.yukawa.kyoto-u.ac.jp/~qimg2023/week2.php.
T. Hartman, C.A. Keller and B. Stoica, Universal Spectrum of 2d Conformal Field Theory in the Large c Limit, JHEP 09 (2014) 118 [arXiv:1405.5137] [INSPIRE].
G. Penington, S.H. Shenker, D. Stanford and Z. Yang, Replica wormholes and the black hole interior, JHEP 03 (2022) 205 [arXiv:1911.11977] [INSPIRE].
D. Stanford, More quantum noise from wormholes, arXiv:2008.08570 [INSPIRE].
S. Choi, S. Kim and J. Song, Supersymmetric Spectral Form Factor and Euclidean Black Holes, Phys. Rev. Lett. 131 (2023) 151602 [arXiv:2206.15357] [INSPIRE].
D. Kapec, R. Mahajan and D. Stanford, Matrix ensembles with global symmetries and ’t Hooft anomalies from 2d gauge theory, JHEP 04 (2020) 186 [arXiv:1912.12285] [INSPIRE].
L.V. Iliesiu, On 2D gauge theories in Jackiw-Teitelboim gravity, arXiv:1909.05253 [INSPIRE].
J. Cotler and K. Jensen, A precision test of averaging in AdS/CFT, JHEP 11 (2022) 070 [arXiv:2205.12968] [INSPIRE].
Y. Chen, V. Ivo and J. Maldacena, Comments on the double cone wormhole, arXiv:2310.11617 [INSPIRE].
D. Stanford and E. Witten, JT gravity and the ensembles of random matrix theory, Adv. Theor. Math. Phys. 24 (2020) 1475 [arXiv:1907.03363] [INSPIRE].
C. Yan, More on torus wormholes in 3d gravity, JHEP 11 (2023) 039 [arXiv:2305.10494] [INSPIRE].
E. Witten, Anomalies and Nonsupersymmetric D-Branes, arXiv:2305.01012 [INSPIRE].
S.R. Coleman, J. Preskill and F. Wilczek, Quantum hair on black holes, Nucl. Phys. B 378 (1992) 175 [hep-th/9201059] [INSPIRE].
N. Arkani-Hamed, S. Dubovsky, A. Nicolis and G. Villadoro, Quantum Horizons of the Standard Model Landscape, JHEP 06 (2007) 078 [hep-th/0703067] [INSPIRE].
N. Benjamin, J. Lee, H. Ooguri and D. Simmons-Duffin, Universal asymptotics for high energy CFT data, JHEP 03 (2024) 115 [arXiv:2306.08031] [INSPIRE].
J. Maldacena, G.J. Turiaci and Z. Yang, Two dimensional Nearly de Sitter gravity, JHEP 01 (2021) 139 [arXiv:1904.01911] [INSPIRE].
I. Bah, Y. Chen and J. Maldacena, Estimating global charge violating amplitudes from wormholes, JHEP 04 (2023) 061 [arXiv:2212.08668] [INSPIRE].
Y. Chen, Spectral form factor for free large N gauge theory and strings, JHEP 06 (2022) 137 [arXiv:2202.04741] [INSPIRE].
Acknowledgments
We thank Tom Hartman, Shota Komatsu, Henry Lin, Juan Maldacena, Miguel Montero, Sridip Pal, Douglas Stanford, Edward Witten for discussion. We specially thank Juan Maldacena for initial collaboration. YC is supported by a Procter Fellowship from Princeton University. GJTs work was supported by the Institute for Advanced Study and the NSF under Grant No. PHY-2207584, and by the Sivian Fund, and currently by the University of Washington and the DOE award DE-SC0024363.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2309.03478
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Chen, Y., Turiaci, G.J. Spin-statistics for black hole microstates. J. High Energ. Phys. 2024, 135 (2024). https://doi.org/10.1007/JHEP04(2024)135
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP04(2024)135