The Schwarzian theory — origins
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A bstract: In this paper we further study the 1d Schwarzian theory, the universal low-energy limit of Sachdev-Ye-Kitaev models, using the link with 2d Liouville theory. We provide a path-integral derivation of the structural link between both theories, and study the relation between 3d gravity, 2d Jackiw-Teitelboim gravity, 2d Liouville and the 1d Schwarzian. We then generalize the Schwarzian double-scaling limit to rational models, relevant for SYK-type models with internal symmetries. We identify the holographic gauge theory as a 2d BF theory and compute correlators of the holographically dual 1d particle-on-a-group action, decomposing these into diagrammatic building blocks, in a manner very similar to the Schwarzian theory.
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The disk partition function and the disk partition function with a single Wilson line insertion in the BF model are given by equations (3.88, 3.89).
“The result of the disk partition function, and that with a single Wilson line insertion, in this model are given by (Mertens 2018; Blommaert et al. 2018; Iliesiu et al. 2019):3.883.89”
From Solvable models of quantum black holes: a review on Jackiw–Teitelboim gravity (2023) · cites this paper as Mertens 2018
In the BF model, 3j-symbols and 6j-symbols can appear for Wilson line endpoints and bulk crossings respectively.
“Finally, the 3j-symbols ( in the above example), and 6j-symbols can appear for Wilson line endpoints and bulk crossings respectively (Mertens 2018; Blommaert et al. 2018; Iliesiu et al. 2019).”
From Solvable models of quantum black holes: a review on Jackiw–Teitelboim gravity (2023) · cites this paper as Mertens 2018
For a group G BF model on a manifold with boundary, including the boundary term and condition yields a well-defined variational principle.
“For a group G BF model on a manifold with a boundary , we can include the boundary term and condition (Mertens 2018):3.86With this boundary term, we have a well-defined variational principle.”
From Solvable models of quantum black holes: a review on Jackiw–Teitelboim gravity (2023) · cites this paper as Mertens 2018
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Gapless spin-fluid ground state in a random quantum Heisenberg magnet
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Solving the Schwarzian via the conformal bootstrap
Mertens, T. G., Turiaci, G. J., & Verlinde, H. L. (2017) · Journal of High Energy Physics · doi:10.1007/jhep08(2017)136 · Cited by 357 · see citing works
Self-citationSachdev–Ye–Kitaev model as Liouville quantum mechanics
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Nearly AdS2 sugra and the super-Schwarzian
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On the dynamics of near-extremal black holes
Nayak, P., Shukla, A., Soni, R. M., Trivedi, S. P., & Vishal, V. (2018) · Journal of High Energy Physics · doi:10.1007/jhep09(2018)048 · Cited by 206 · see citing works
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
Self-citationA universal Schwarzian sector in two-dimensional conformal field theories
Ghosh, A., Maxfield, H., & Turiaci, G. J. (2020) · Journal of High Energy Physics · doi:10.1007/jhep05(2020)104 · Cited by 135 · see citing works
Liouville quantum gravity — holography, JT and matrices
Mertens, T. G., & Turiaci, G. J. (2021) · Journal of High Energy Physics · doi:10.1007/jhep01(2021)073 · Cited by 130 · see citing works
Self-citationDoes the SYK model have a spin glass phase?
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Towards black hole evaporation in Jackiw-Teitelboim gravity
Mertens, T. G. (2019) · Journal of High Energy Physics · doi:10.1007/jhep07(2019)097 · Cited by 41 · see citing works
Self-citationOn 2D gauge theories in Jackiw-Teitelboim gravity
Iliesiu, L. V. (2019) · arXiv · doi:10.48550/arxiv.1909.05253 · Cited by 33 · see citing works
Joshi, L. K., Mukhopadhyay, A., & Soloviev, A. (2020) · Physical Review D · doi:10.1103/physrevd.101.066001 · Cited by 10 · see citing works
- Authors
- Mertens, T. G.
- Affiliations
- Princeton University (US)
- Corresponding author
- Mertens, Thomas G.
- ORCID
- Mertens, Thomas G.
- Venue
- Journal of High Energy Physics
- Published
- 2018-05
- Volume
- 2018
- Issue
- 5
- ISSN
- 1029-8479 (ISSN-L)
- OpenAlex
- W2785462095
- Cited by
- 162
- References
- 7
- Citations by year
- 2026: 12 · 2025: 14 · 2024: 14 · 2023: 17 · 2022: 28 · 2021: 20 · 2020: 19 · 2019: 26 · 2018: 12
- FWCI
- 10.20
- Type
- journal article
- Language
- en
- Open access
- diamond
- doi.org
- Licence
- Locations
- Journal of High Energy Physics (publishedVersion, cc-by)
- arXiv (Cornell University) (publishedVersion)
- Ghent University Academic Bibliography (Ghent University) (submittedVersion, cc-by)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- arXiv (Cornell University)
- Funders
- Fonds Wetenschappelijk Onderzoek
- Vlaamse regering
- Topics
- 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
- Physical Sciences › Mathematics › Geometry and Topology › Algebraic structures and combinatorial models
- Keywords
- Schwarzian theory, Sachdev-Ye-Kitaev model, Liouville theory, Jackiw-Teitelboim gravity, double scaling limit, rational model, BF theory, holographic gauge theory, path integral, three-dimensional gravity, low-energy limit
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