Abstract
The dynamics of a nearly-AdS2 spacetime with boundaries is reduced to that of two particles in the anti-de Sitter space. We determine the class of physically meaningful wavefunctions, and prescribe the statistical mechanics of a black hole. We demonstrate how wavefunctions for a two-sided black hole and a regularized notion of trace can be used to construct thermal partition functions, and more generally, arbitrary density matrices. We also obtain correlation functions of external operators.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
R. Jackiw, Lower dimensional gravity, Nucl. Phys. B 252 (1985) 343 [INSPIRE].
C. Teitelboim, Gravitation and Hamiltonian structure in two space-time dimensions, Phys. Lett. B 126 (1983) 41.
A. Almheiri and J. Polchinski, Models of AdS 2 backreaction and holography, JHEP 11 (2015) 014 [arXiv:1402.6334] [INSPIRE].
J.B. Hartle and S.W. Hawking, Wave function of the Universe, Phys. Rev. D 28 (1983) 2960.
S. Sachdev and J. Ye, Gapless spin fluid ground state in a random, quantum Heisenberg magnet, Phys. Rev. Lett. 70 (1993) 3339 [cond-mat/9212030] [INSPIRE].
A. Kitaev, A simple model of quantum holography, talks given at KITP, April 7 and May 27 (2015).
A. Kitaev and S.J. Suh, The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual, JHEP 05 (2018) 183 [arXiv:1711.08467] [INSPIRE].
J. Maldacena and D. Stanford, Remarks on the Sachdev-Ye-Kitaev model, Phys. Rev. D 94 (2016) 106002 [arXiv:1604.07818] [INSPIRE].
J.S. Cotler et al., Black holes and random matrices, JHEP 05 (2017) 118 [Erratum ibid. 09 (2018) 002] [arXiv:1611.04650] [INSPIRE].
D. Stanford and E. Witten, Fermionic localization of the Schwarzian theory, JHEP 10 (2017) 008 [arXiv:1703.04612] [INSPIRE].
D. Bagrets, A. Altland and A. Kamenev, Sachdev-Ye-Kitaev model as Liouville quantum mechanics, Nucl. Phys. B 911 (2016) 191 [arXiv:1607.00694] [INSPIRE].
D. Bagrets, A. Altland and A. Kamenev, Power-law out of time order correlation functions in the SYK model, Nucl. Phys. B 921 (2017) 727 [arXiv:1702.08902] [INSPIRE].
T.G. Mertens, G.J. Turiaci and H.L. Verlinde, Solving the Schwarzian via the conformal bootstrap, JHEP 08 (2017) 136 [arXiv:1705.08408] [INSPIRE].
K. Jensen, Chaos in AdS 2 holography, Phys. Rev. Lett. 117 (2016) 111601 [arXiv:1605.06098] [INSPIRE].
J. Maldacena, D. Stanford and Z. Yang, Conformal symmetry and its breaking in two dimensional Nearly Anti-de-Sitter space, PTEP 2016 (2016) 12C104 [arXiv:1606.01857] [INSPIRE].
J. Engelsöy, T.G. Mertens and H. Verlinde, An investigation of AdS 2 backreaction and holography, JHEP 07 (2016) 139 [arXiv:1606.03438] [INSPIRE].
D. Harlow and D. Jafferis, The factorization problem in Jackiw-Teitelboim gravity, arXiv:1804.01081 [INSPIRE].
J. Lin, Entanglement entropy in Jackiw-Teitelboim gravity, arXiv:1807.06575 [INSPIRE].
A. Kitaev, Notes on \( \tilde{\mathrm{SL}}\left(2,\mathbb{R}\right) \) representations, arXiv:1711.08169 [INSPIRE].
A.M. Polyakov, Gauge fields and strings, Contemp. Concepts Phys. 3 (1987) 1.
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1808.07032
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Kitaev, A., Suh, S.J. Statistical mechanics of a two-dimensional black hole. J. High Energ. Phys. 2019, 198 (2019). https://doi.org/10.1007/JHEP05(2019)198
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP05(2019)198