Matrix models and deformations of JT gravity
Open accessAbstract
Recently, it has been found that Jackiw-Teitelboim (JT) gravity, which is a two-dimensional theory with bulk action − 1 / 2 ∫ d 2 x g ϕ ( R + 2 ) , is dual to a matrix model, that is, a random ensemble of quantum systems rather than a specific quantum mechanical system. In this article, we argue that a deformation of JT gravity with bulk action − 1 / 2 ∫ d 2 x g ( ϕ R + W ( ϕ ) ) is likewise dual to a matrix model. With a specific procedure for defining the path integral of the theory, we determine the density of eigenvalues of the dual matrix model. There is a simple answer if W (0) = 0, and otherwise a rather complicated answer.
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A duality similar to the JT case between pure 2d dilaton gravity and a matrix integral was proven in Maxfield and Turiaci (2021) and independently in Witten (2020).
“This duality was proven in Maxfield and Turiaci (2021) and independently in Witten (2020), and a precise relation was found between these two functions.”
From Solvable models of quantum black holes: a review on Jackiw–Teitelboim gravity (2023) · cites this paper as Witten (2020)
Cites
Brézin, E., Itzykson, C., Parisi, G., & Zuber, J. B. (1978) · Communications in Mathematical Physics · doi:10.1007/bf01614153 · Cited by 1,479 · see citing works
Two-dimensional quantum gravity in Minkowski space
Banks, T., & O'Loughlin, M. (1991) · Nuclear Physics B · doi:10.1016/0550-3213(91)90547-b · Cited by 192 · see citing works
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Solvable models of quantum black holes: a review on Jackiw–Teitelboim gravity
Mertens, T. G., & Turiaci, G. J. (2023) · Living Reviews in Relativity · doi:10.1007/s41114-023-00046-1 · Cited by 181 · see citing works
2D dilaton-gravity, deformations of the minimal string, and matrix models
Turiaci, G. J., Usatyuk, M., & Weng, W. W. (2021) · Classical and Quantum Gravity · doi:10.1088/1361-6382/ac25df · Cited by 73 · see citing works
Free energy for deformed Jackiw-Teitelboim gravity
Alishahiha, M., Faraji Astaneh, A., Jafari, G., Naseh, A., & Taghavi, B. (2021) · Physical Review D · doi:10.1103/physrevd.103.046005 · Cited by 29 · see citing works
- Authors
- Witten, E.
- Affiliations
- Institute for Advanced Study (US)
- Corresponding author
- Witten, Edward
- ORCID
- Witten, Edward
- Venue
- Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- Publisher
- The Royal Society
- Published
- 2020-12
- Volume
- 476
- Issue
- 2244
- Pages
- 20200582-20200582
- ISSN
- 1364-5021 (ISSN-L)
- 1471-2946
- PMC
- PMC7776967
- OpenAlex
- W3037844630
- Cited by
- 89
- References
- 2
- Citations by year
- 2026: 2 · 2025: 4 · 2024: 11 · 2023: 16 · 2022: 23 · 2021: 31 · 2020: 2
- FWCI
- 7.96
- Type
- journal article
- Language
- en
- Open access
- green
- www.ncbi.nlm.nih.gov
- Licence
- Locations
- Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences (publishedVersion)
- PubMed Central (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- United States National Science Foundation (PHY-1911298)
- Topics
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Physical Sciences › Mathematics › Statistics and Probability › Random Matrices and Applications
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Keywords
- Jackiw-Teitelboim gravity, matrix models, two-dimensional gravity, random matrix ensembles, eigenvalue density, path integral
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