Abstract
For ensembles of Hamiltonians that fall under the Dyson classification of random matrices with β ∈ {1, 2, 4}, the low-temperature mean entropy can be shown to vanish as 〈S(T)〉 ∼ κTβ + 1. A similar relation holds for Altland-Zirnbauer ensembles. JT gravity has been shown to be dual to the double-scaling limit of a β = 2 ensemble, with a classical eigenvalue density \( \propto {e}^{S_0}\sqrt{E} \) when 0 < E ≪ 1. We use universal results about the distribution of the smallest eigenvalues in such ensembles to calculate κ up to corrections that we argue are doubly exponentially small in S0.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S. F. Edwards and P. W. Anderson, Theory of spin glasses, J. Phys. F 5 (1975) 965.
N. Engelhardt, S. Fischetti and A. Maloney, Free energy from replica wormholes, Phys. Rev. D 103 (2021) 046021 [arXiv:2007.07444] [INSPIRE].
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 [INSPIRE].
P. Saad, S. H. Shenker and D. Stanford, JT gravity as a matrix integral, arXiv:1903.11115 [INSPIRE].
D. Stanford and E. Witten, JT Gravity and the Ensembles of Random Matrix Theory, arXiv:1907.03363 [INSPIRE].
K. Okuyama, Replica symmetry breaking in random matrix model: a toy model of wormhole networks, Phys. Lett. B 803 (2020) 135280 [arXiv:1903.11776] [INSPIRE].
K. Okuyama and K. Sakai, JT gravity, KdV equations and macroscopic loop operators, JHEP 01 (2020) 156 [arXiv:1911.01659] [INSPIRE].
K. Okuyama and K. Sakai, Multi-boundary correlators in JT gravity, JHEP 08 (2020) 126 [arXiv:2004.07555] [INSPIRE].
C. V. Johnson, Explorations of nonperturbative Jackiw-Teitelboim gravity and supergravity, Phys. Rev. D 103 (2021) 046013 [arXiv:2006.10959] [INSPIRE].
C. V. Johnson, Low Energy Thermodynamics of JT Gravity and Supergravity, arXiv:2008.13120 [INSPIRE].
K. Okuyama, Quenched free energy in random matrix model, JHEP 12 (2020) 080 [arXiv:2009.02840] [INSPIRE].
K. Okuyama, Quenched free energy from spacetime D-branes, JHEP 03 (2021) 073 [arXiv:2101.05990] [INSPIRE].
A. B. J. Kuijlaars, Universality, arXiv:1103.5922.
C. A. Tracy and H. Widom, Level spacing distributions and the Airy kernel, Commun. Math. Phys. 159 (1994) 151 [hep-th/9211141] [INSPIRE].
N. S. Witte, F. Bornemann and P. J. Forrester, Joint distribution of the first and second eigenvalues at the soft edge of unitary ensembles, Nonlinearity 26 (2013) 1799 [arXiv:1209.2190].
A. Perret and G. Schehr, Near-extreme eigenvalues and the first gap of hermitian random matrices, J. Stat. Phys. 156 (2014) 843.
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].
D. Stanford and E. Witten, Fermionic Localization of the Schwarzian Theory, JHEP 10 (2017) 008 [arXiv:1703.04612] [INSPIRE].
B. Eynard, T. Kimura and S. Ribault, Random matrices, arXiv:1510.04430 [INSPIRE].
G. ’t Hooft, A Planar Diagram Theory for Strong Interactions, Nucl. Phys. B 72 (1974) 461 [INSPIRE].
E. Brézin, C. Itzykson, G. Parisi and J. B. Zuber, Planar Diagrams, Commun. Math. Phys. 59 (1978) 35 [INSPIRE].
F. J. Dyson, Statistical theory of the energy levels of complex systems. I, J. Math. Phys. 3 (1962) 140 [INSPIRE].
A. Altland and M. R. Zirnbauer, Nonstandard symmetry classes in mesoscopic normal-superconducting hybrid structures, Phys. Rev. B 55 (1997) 1142 [cond-mat/9602137] [INSPIRE].
C. Nadal and S. N. Majumdar, A simple derivation of the Tracy-Widom distribution of the maximal eigenvalue of a Gaussian unitary random matrix, J. Stat. Mech. 1104 (2011) P04001 [arXiv:1102.0738] [INSPIRE].
P. Deift, A. Its and I. Krasovsky, Asymptotics of the Airy-kernel determinant, math/0609451.
C. A. Tracy and H. Widom, On orthogonal and symplectic matrix ensembles, Commun. Math. Phys. 177 (1996) 727 [solv-int/9509007] [INSPIRE].
T. Nagao and K. Slevin, Nonuniversal correlations for random matrix ensembles, J. Math. Phys 34 (1993) 2075.
C. A. Tracy and H. Widom, Level spacing distributions and the Bessel kernel, Commun. Math. Phys. 161 (1994) 289 [hep-th/9304063] [INSPIRE].
P. J. Forrester and N. S. Witte, The Distribution of the first Eigenvalue Spacing at the Hard Edge of the Laguerre Unitary Ensemble, arXiv:0704.1926.
C. V. Johnson, On the Quenched Free Energy of JT Gravity and Supergravity, arXiv:2104.02733 [INSPIRE].
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: 2103.03896
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
Janssen, O., Mirbabayi, M. Low-temperature entropy in JT gravity. J. High Energ. Phys. 2021, 74 (2021). https://doi.org/10.1007/JHEP06(2021)074
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP06(2021)074