Free energy for deformed Jackiw-Teitelboim gravity
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In this paper, we study a particular deformation of the Jackiw-Teitelboim gravity recently considered by Maxfield, Turiaci, and independently by Witten. We will compute the partition function of this model as well as its higher order correlators to all orders in genus expansion in the low temperature limit for small perturbations. In this limit, the results match with those obtained from the Airy limit of a Hermitian random matrix ensemble. Using this result, we will also study the free energy of the model. One observes that although the annealed free energy has pathological behaviors, under certain assumptions, the quenched free energy evaluated by replica trick exhibits the desired properties at low temperatures.
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For the free energy of a system, one should compute the quenched free energy, not the annealed free energy, where the brackets denote the gravitational path integral.
“For example, for the free energy of the system, one should compute the quenched free energy , and not the annealed free energy , where the brackets denote the gravitational path integral.”
From Solvable models of quantum black holes: a review on Jackiw–Teitelboim gravity (2023) · cites this paper as Alishahiha et al. 2021
Cites
Callan, C. G., Giddings, S. B., Harvey, J. A., & Strominger, A. (1992) · Physical Review D · doi:10.1103/physrevd.45.r1005 · Cited by 1,131 · see citing works
Jackiw, R. (1985) · Nuclear Physics B · doi:10.1016/0550-3213(85)90448-1 · Cited by 1,111 · see citing works
Gravitation and hamiltonian structure in two spacetime dimensions
Teitelboim, C. (1983) · Physics Letters B · doi:10.1016/0370-2693(83)90012-6 · Cited by 1,064 · see citing works
Entanglement wedge reconstruction and the information paradox
Penington, G. (2020) · Journal of High Energy Physics · doi:10.1007/jhep09(2020)002 · Cited by 968 · see citing works
Replica wormholes and the entropy of Hawking radiation
Almheiri, A., Hartman, T., Maldacena, J., Shaghoulian, E., & Tajdini, A. (2020) · Journal of High Energy Physics · doi:10.1007/jhep05(2020)013 · Cited by 910 · cited 2× · see citing works
“In fact, the situation is very similar to that of the island formula for fine grained entropy of evaporating black holes [4, 5].”
BackgroundThe entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole
Almheiri, A., Engelhardt, N., Marolf, D., & Maxfield, H. (2019) · Journal of High Energy Physics · doi:10.1007/jhep12(2019)063 · Cited by 818 · see citing works
Replica wormholes and the black hole interior
Penington, G., Shenker, S. H., Stanford, D., & Yang, Z. (2019) · arXiv · doi:10.48550/arxiv.1911.11977 · Cited by 809
Replica wormholes and the black hole interior
Penington, G., Shenker, S. H., Stanford, D., & Yang, Z. (2022) · Journal of High Energy Physics · doi:10.1007/jhep03(2022)205 · Cited by 807 · see citing works
The Page curve of Hawking radiation from semiclassical geometry
Almheiri, A., Mahajan, R., Maldacena, J., & Zhao, Y. (2020) · Journal of High Energy Physics · doi:10.1007/jhep03(2020)149 · Cited by 749 · see citing works
The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole
Almheiri, A., Engelhardt, N., Marolf, D. M., & Maxfield, H. (2019) · eScholarship (California Digital Library) · Cited by 734 · see citing works
The spectrum edge of random matrix ensembles
Forrester, P. J. (1993) · Nuclear Physics B · doi:10.1016/0550-3213(93)90126-a · Cited by 538 · see citing works
Strings in less than one dimension and the generalized KdV hierarchies
Douglas, M. R. (1990) · Physics Letters B · doi:10.1016/0370-2693(90)91716-o · Cited by 512 · see citing works
Gelfand, I. M., & Dikii, L. A. (1975) · Russian Mathematical Surveys · doi:10.1070/rm1975v030n05abeh001522 · Cited by 494 · see citing works
JT gravity as a matrix integral
Saad, P., Shenker, S. H., & Stanford, D. (2019) · arXiv · doi:10.48550/arxiv.1903.11115 · Cited by 442 · see citing works
A nonperturbative treatment of two-dimensional quantum gravity
Gross, D. J., & Migdal, A. (1990) · Nuclear Physics B · doi:10.1016/0550-3213(90)90450-r · Cited by 430 · see citing works
Simple geodesics and Weil-Petersson volumes of moduli spaces of bordered Riemann surfaces
Mirzakhani, M. (2006) · Inventiones mathematicae · doi:10.1007/s00222-006-0013-2 · Cited by 369 · see citing works
The Page curve of Hawking radiation from semiclassical geometry
Almheiri, A. (2023) · OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) · doi:10.1007/jhep03%282020%29149 · Cited by 324 · see citing works
Weil-Petersson volumes and intersection theory on the moduli space of curves
Mirzakhani, M. (2006) · Journal of the American Mathematical Society · doi:10.1090/s0894-0347-06-00526-1 · Cited by 294 · see citing works
Microscopic and macroscopic loops in non-perturbative two dimensional gravity
Banks, T., Douglas, M. R., Nathan Seiberg, B., & Shenker, S. H. (1990) · Physics Letters B · doi:10.1016/0370-2693(90)91736-u · Cited by 254 · see citing works
The path integral of 3D gravity near extremality; or, JT gravity with defects as a matrix integral
Maxfield, H., & Turiaci, G. J. (2021) · Journal of High Energy Physics · doi:10.1007/jhep01(2021)118 · Cited by 209 · see citing works
Almheiri, A., Mahajan, R., & Maldacena, J. (2019) · arXiv · doi:10.48550/arxiv.1910.11077 · Cited by 191 · see citing works
Defects in Jackiw-Teitelboim quantum gravity
Mertens, T. G., & Turiaci, G. J. (2019) · Journal of High Energy Physics · doi:10.1007/jhep08(2019)127 · Cited by 115 · see citing works
Growth of Weil-Petersson Volumes and Random Hyperbolic Surface of Large Genus
Mirzakhani, M. (2013) · Journal of Differential Geometry · doi:10.4310/jdg/1367438650 · Cited by 112 · see citing works
JT gravity, KdV equations and macroscopic loop operators
Okuyama, K., & Sakai, K. (2020) · Journal of High Energy Physics · doi:10.1007/jhep01(2020)156 · Cited by 97 · see citing works
Nonperturbative Jackiw-Teitelboim gravity
Johnson, C. V. (2020) · Physical Review D · doi:10.1103/physrevd.101.106023 · Cited by 92 · see citing works
Weil-Petersson volume of moduli spaces, Mirzakhani's recursion and matrix models
Eynard, B., & Orantin, N. (2007) · arXiv · doi:10.48550/arxiv.0705.3600 · Cited by 91 · see citing works
Free energy from replica wormholes
Engelhardt, N., Fischetti, S., & Maloney, A. (2021) · Physical Review D · doi:10.1103/physrevd.103.046021 · Cited by 90 · cited 5× · see citing works
“nsed matter physics literature, a better quantity one may dene is the quenched free energy which we shall study it in what follows. To compute the quenched free energy for JT gravity, the authors of [6] have used a certain replica trick. In the present case, we will consider the same method to compute the quench free…”
BackgroundMethodInfluentialMatrix models and deformations of JT gravity
Witten, E. (2020) · Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences · doi:10.1098/rspa.2020.0582 · Cited by 89 · see citing works
Deformations of JT Gravity and Phase TransitionsPreprint
Witten, E. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2006.03494 · Cited by 82 · see citing works
Unitarity from a smooth horizon?
Bousso, R., & Tomašević, M. (2020) · Physical Review D · doi:10.1103/physrevd.102.106019 · Cited by 80 · see citing works
Flat space holography and the complex Sachdev-Ye-Kitaev model
Afshar, H., González, H. A., Grumiller, D., & Vassilevich, D. (2020) · Physical Review D · doi:10.1103/physrevd.101.086024 · Cited by 76 · see citing works
Generalizations of McShane's identity to hyperbolic cone-surfaces
Tan, S. P., Wong, Y. L., & Zhang, Y. (2006) · Journal of Differential Geometry · doi:10.4310/jdg/1143593126 · Cited by 70 · see citing works
Explorations of nonperturbative Jackiw-Teitelboim gravity and supergravity
Johnson, C. V. (2021) · Physical Review D · doi:10.1103/physrevd.103.046013 · Cited by 65 · see citing works
Jackiw-Teitelboim supergravity, minimal strings, and matrix models
Johnson, C. V. (2021) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.103.046012 · Cited by 59 · see citing works
Correlation functions of the KdV hierarchy and applications to intersection numbers over M¯g,n
Bertola, M., Dubrovin, B., & Yang, D. (2016) · Physica D Nonlinear Phenomena · doi:10.1016/j.physd.2016.04.008 · Cited by 53 · see citing works
Multi-boundary correlators in JT gravity
Okuyama, K., & Sakai, K. (2020) · Journal of High Energy Physics · doi:10.1007/jhep08(2020)126 · Cited by 52 · see citing works
On the large genus asymptotics of Weil-Petersson volumesPreprint
Zograf, P. (2008) · arXiv (Cornell University) · doi:10.48550/arxiv.0812.0544 · Cited by 37 · see citing works
Connected correlator of 1/2 BPS Wilson loops in $$ \mathcal{N}=4 $$ SYM
Okuyama, K. (2018) · Journal of High Energy Physics · doi:10.1007/jhep10(2018)037 · Cited by 28 · see citing works
Moduli spaces of hyperbolic surfaces and their Weil-Petersson volumesPreprint
Do, N. (2011) · arXiv (Cornell University) · doi:10.48550/arxiv.1103.4674 · Cited by 24 · see citing works
Low Energy Thermodynamics of JT Gravity and SupergravityPreprint
Johnson, C. V. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2008.13120 · Cited by 19 · see citing works
Generating functions for intersection numbers on moduli spaces of curves
Okounkov, A. (2001) · arXiv · doi:10.48550/arxiv.math/0101201 · Cited by 17 · see citing works
JT gravity and the asymptotic Weil–Petersson volume
Kimura, Y. (2020) · Physics Letters B · doi:10.1016/j.physletb.2020.135989 · Cited by 14 · see citing works
Non-Perturbative JT GravityPreprint
Johnson, C. V. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1912.03637 · Cited by 13 · see citing works
Connected correlator of 1/2 BPS Wilson loops in N=4 SYM
Okuyama, K. (2018) · SOAR (Shinshu University) · Cited by 11 · see citing works
Momeni, D. (2021) · The European Physical Journal C · doi:10.1140/epjc/s10052-021-08985-1 · Cited by 11 · see citing works
Quenched free energy in random matrix model
Okuyama, K. (2020) · Journal of High Energy Physics · doi:10.1007/jhep12(2020)080 · Cited by 7 · see citing works
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- Authors
- Alishahiha, M., Faraji Astaneh, A., Jafari, G., Naseh, A., & Taghavi, B.
- Affiliations
- Institute for Research in Fundamental Sciences (IR)
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 2021-02-08
- Volume
- 103
- Issue
- 4
- ISSN
- 2470-0010 (ISSN-L)
- 2470-0029
- OpenAlex
- W3089482410
- Cited by
- 29
- References
- 45
- Citations by year
- 2025: 2 · 2024: 4 · 2023: 4 · 2022: 8 · 2021: 11
- FWCI
- 5.05
- Type
- journal article
- Language
- en
- Open access
- hybrid
- doi.org
- Licence
- Locations
- Physical review. D/Physical review. D. (publishedVersion, cc-by)
- arXiv (Cornell University) (publishedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Random Matrices and Applications
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Keywords
- Jackiw-Teitelboim gravity, free energy, partition function, genus expansion, quenched free energy, replica method, low-temperature limit, two-dimensional gravity
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