Abstract
In this paper we study a connection between Jackiw-Teitelboim (JT) gravity on two-dimensional anti de-Sitter spaces and a semiclassical limit of c < 1 two-dimensional string theory. The world-sheet theory of the latter consists of a space-like Liouville CFT coupled to a non-rational CFT defined by a time-like Liouville CFT. We show that their actions, disk partition functions and annulus amplitudes perfectly agree with each other, where the presence of boundary terms plays a crucial role. We also reproduce the boundary Schwarzian theory from the Liouville theory description. Then, we identify a matrix model dual of our two-dimensional string theory with a specific time-dependent background in c = 1 matrix quantum mechanics. Finally, we also explain the corresponding relation for the two-dimensional de-Sitter JT gravity.
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 [INSPIRE].
A. Almheiri and J. Polchinski, Models of AdS2 backreaction and holography, JHEP 11 (2015) 014 [arXiv:1402.6334] [INSPIRE].
K. Jensen, Chaos in AdS2 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 AdS2 backreaction and holography, JHEP 07 (2016) 139 [arXiv:1606.03438] [INSPIRE].
A. Ghosh, H. Maxfield and G.J. Turiaci, A universal Schwarzian sector in two-dimensional conformal field theories, JHEP 05 (2020) 104 [arXiv:1912.07654] [INSPIRE].
S. Sachdev, Universal low temperature theory of charged black holes with AdS2 horizons, J. Math. Phys. 60 (2019) 052303 [arXiv:1902.04078] [INSPIRE].
G. Penington, S.H. Shenker, D. Stanford and Z. Yang, Replica wormholes and the black hole interior, arXiv:1911.11977 [INSPIRE].
A. Almheiri, T. Hartman, J. Maldacena, E. Shaghoulian and A. Tajdini, Replica Wormholes and the Entropy of Hawking Radiation, JHEP 05 (2020) 013 [arXiv:1911.12333] [INSPIRE].
V. Balasubramanian, A. Kar and T. Ugajin, Entanglement between two disjoint universes, JHEP 02 (2021) 136 [arXiv:2008.05274] [INSPIRE].
K. Goto, T. Hartman and A. Tajdini, Replica wormholes for an evaporating 2D black hole, JHEP 04 (2021) 289 [arXiv:2011.09043] [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, Adv. Theor. Math. Phys. 24 (2020) 1475 [arXiv:1907.03363] [INSPIRE].
P. Saad, Late Time Correlation Functions, Baby Universes, and ETH in JT Gravity, arXiv:1910.10311 [INSPIRE].
Y. Kimura, JT gravity and the asymptotic Weil-Petersson volume, Phys. Lett. B 811 (2020) 135989 [arXiv:2008.04141] [INSPIRE].
Y. Kimura, Correlation functions with multiple boundaries in JT gravity and resolvents, arXiv:2106.11856 [INSPIRE].
C.V. Johnson, Nonperturbative Jackiw-Teitelboim gravity, Phys. Rev. D 101 (2020) 106023 [arXiv:1912.03637] [INSPIRE].
A. Blommaert, T.G. Mertens and H. Verschelde, Eigenbranes in Jackiw-Teitelboim gravity, JHEP 02 (2021) 168 [arXiv:1911.11603] [INSPIRE].
N. Afkhami-Jeddi, H. Cohn, T. Hartman and A. Tajdini, Free partition functions and an averaged holographic duality, JHEP 01 (2021) 130 [arXiv:2006.04839] [INSPIRE].
A. Maloney and E. Witten, Averaging over Narain moduli space, JHEP 10 (2020) 187 [arXiv:2006.04855] [INSPIRE].
J. Cotler and K. Jensen, AdS3 gravity and random CFT, JHEP 04 (2021) 033 [arXiv:2006.08648] [INSPIRE].
J. Cotler and K. Jensen, AdS3 wormholes from a modular bootstrap, JHEP 11 (2020) 058 [arXiv:2007.15653] [INSPIRE].
P.H. Ginsparg and G.W. Moore, Lectures on 2-D gravity and 2-D string theory, in Theoretical Advanced Study Institute (TASI 92): From Black Holes and Strings to Particles, (1993), pp. 277–469 [hep-th/9304011] [INSPIRE].
P. Di Francesco, P.H. Ginsparg and J. Zinn-Justin, 2-D Gravity and random matrices, Phys. Rept. 254 (1995) 1 [hep-th/9306153] [INSPIRE].
S. Alexandrov, Matrix quantum mechanics and two-dimensional string theory in nontrivial backgrounds, other thesis, 9, 2003 [hep-th/0311273] [INSPIRE].
N. Seiberg and D. Shih, Minimal string theory, Comptes Rendus Physique 6 (2005) 165 [hep-th/0409306] [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].
N. Seiberg and D. Stanford, unpublished.
T.G. Mertens and G.J. Turiaci, Liouville quantum gravity — holography, JT and matrices, JHEP 01 (2021) 073 [arXiv:2006.07072] [INSPIRE].
G.J. Turiaci, M. Usatyuk and W.W. Weng, Dilaton-gravity, deformations of the minimal string, and matrix models, arXiv:2011.06038 [INSPIRE].
E. Casali, D. Marolf, H. Maxfield and M. Rangamani, Baby Universes and Worldline Field Theories, arXiv:2101.12221 [INSPIRE].
P. Di Francesco, P. Mathieu and D. Senechal, Conformal Field Theory, Graduate Texts in Contemporary Physics, Springer-Verlag, New York (1997), [DOI] [INSPIRE].
D. Kapec and R. Mahajan, Comments on the quantum field theory of the Coulomb gas formalism, JHEP 04 (2021) 136 [arXiv:2010.10428] [INSPIRE].
M. Gutperle and A. Strominger, Time - like boundary Liouville theory, Phys. Rev. D 67 (2003) 126002 [hep-th/0301038] [INSPIRE].
A. Strominger and T. Takayanagi, Correlators in time - like bulk Liouville theory, Adv. Theor. Math. Phys. 7 (2003) 369 [hep-th/0303221] [INSPIRE].
V. Schomerus, Rolling tachyons from Liouville theory, JHEP 11 (2003) 043 [hep-th/0306026] [INSPIRE].
J.L. Karczmarek and A. Strominger, Matrix cosmology, JHEP 04 (2004) 055 [hep-th/0309138] [INSPIRE].
T. Takayanagi, Matrix model and time-like linear dilaton matter, JHEP 12 (2004) 071 [hep-th/0411019] [INSPIRE].
W. McElgin, Notes on Liouville Theory at c ≤ 1, Phys. Rev. D 77 (2008) 066009 [arXiv:0706.0365] [INSPIRE].
D. Harlow, J. Maltz and E. Witten, Analytic Continuation of Liouville Theory, JHEP 12 (2011) 071 [arXiv:1108.4417] [INSPIRE].
N. Seiberg and D. Shih, Branes, rings and matrix models in minimal (super)string theory, JHEP 02 (2004) 021 [hep-th/0312170] [INSPIRE].
D. Kutasov, K. Okuyama, J.-w. Park, N. Seiberg and D. Shih, Annulus amplitudes and ZZ branes in minimal string theory, JHEP 08 (2004) 026 [hep-th/0406030] [INSPIRE].
J.M. Maldacena, G.W. Moore, N. Seiberg and D. Shih, Exact vs. semiclassical target space of the minimal string, JHEP 10 (2004) 020 [hep-th/0408039] [INSPIRE].
I.R. Klebanov, String theory in two-dimensions, in Spring School on String Theory and Quantum Gravity (to be followed by Workshop), (1991) [hep-th/9108019] [INSPIRE].
J. Polchinski, What is string theory?, in NATO Advanced Study Institute: Les Houches Summer School, Session 62: Fluctuating Geometries in Statistical Mechanics and Field Theory, (1994) [hep-th/9411028] [INSPIRE].
G. Mandal, P. Nayak and S.R. Wadia, Coadjoint orbit action of Virasoro group and two-dimensional quantum gravity dual to SYK/tensor models, JHEP 11 (2017) 046 [arXiv:1702.04266] [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].
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].
S.R. Das, A. Ghosh, A. Jevicki and K. Suzuki, Near Conformal Perturbation Theory in SYK Type Models, JHEP 12 (2020) 171 [arXiv:2006.13149] [INSPIRE].
T.G. Mertens and G.J. Turiaci, Defects in Jackiw-Teitelboim Quantum Gravity, JHEP 08 (2019) 127 [arXiv:1904.05228] [INSPIRE].
H. Maxfield and G.J. Turiaci, The path integral of 3D gravity near extremality; or, JT gravity with defects as a matrix integral, JHEP 01 (2021) 118 [arXiv:2006.11317] [INSPIRE].
E. Witten, Matrix Models and Deformations of JT Gravity, Proc. Roy. Soc. Lond. A 476 (2020) 20200582 [arXiv:2006.13414] [INSPIRE].
E. Mefford and K. Suzuki, Jackiw-Teitelboim quantum gravity with defects and the Aharonov-Bohm effect, JHEP 05 (2021) 026 [arXiv:2011.04695] [INSPIRE].
V. Fateev, A.B. Zamolodchikov and A.B. Zamolodchikov, Boundary Liouville field theory. 1. Boundary state and boundary two point function, hep-th/0001012 [INSPIRE].
J. Teschner, Remarks on Liouville theory with boundary, PoS tmr2000 (2000) 041 [hep-th/0009138] [INSPIRE].
K. Okuyama and K. Sakai, FZZT branes in JT gravity and topological gravity, arXiv:2108.03876 [INSPIRE].
J. Maldacena, G.J. Turiaci and Z. Yang, Two dimensional Nearly de Sitter gravity, JHEP 01 (2021) 139 [arXiv:1904.01911] [INSPIRE].
J. Cotler, K. Jensen and A. Maloney, Low-dimensional de Sitter quantum gravity, JHEP 06 (2020) 048 [arXiv:1905.03780] [INSPIRE].
D. Harlow and D. Jafferis, The Factorization Problem in Jackiw-Teitelboim Gravity, JHEP 02 (2020) 177 [arXiv:1804.01081] [INSPIRE].
D. Stanford and E. Witten, Fermionic Localization of the Schwarzian Theory, JHEP 10 (2017) 008 [arXiv:1703.04612] [INSPIRE].
H. Kyono, S. Okumura and K. Yoshida, Deformations of the Almheiri-Polchinski model, JHEP 03 (2017) 173 [arXiv:1701.06340] [INSPIRE].
H. Kyono, S. Okumura and K. Yoshida, Comments on 2D dilaton gravity system with a hyperbolic dilaton potential, Nucl. Phys. B 923 (2017) 126 [arXiv:1704.07410] [INSPIRE].
S. Okumura and K. Yoshida, Weyl transformation and regular solutions in a deformed Jackiw-Teitelboim model, Nucl. Phys. B 933 (2018) 234 [arXiv:1801.10537] [INSPIRE].
A. Goel, L.V. Iliesiu, J. Kruthoff and Z. Yang, Classifying boundary conditions in JT gravity: from energy-branes to α-branes, JHEP 04 (2021) 069 [arXiv:2010.12592] [INSPIRE].
N. Seiberg, Notes on quantum Liouville theory and quantum gravity, Prog. Theor. Phys. Suppl. 102 (1990) 319 [INSPIRE].
P. Betzios and O. Papadoulaki, Liouville theory and Matrix models: A Wheeler DeWitt perspective, JHEP 09 (2020) 125 [arXiv:2004.00002] [INSPIRE].
D.J. Gross and N. Miljkovic, A Nonperturbative Solution of D = 1 String Theory, Phys. Lett. B 238 (1990) 217 [INSPIRE].
E. Brézin, V.A. Kazakov and A.B. Zamolodchikov, Scaling Violation in a Field Theory of Closed Strings in One Physical Dimension, Nucl. Phys. B 338 (1990) 673 [INSPIRE].
P.H. Ginsparg and J. Zinn-Justin, 2D gravity + 1D matter, Phys. Lett. B 240 (1990) 333 [INSPIRE].
S.R. Das and A. Jevicki, String Field Theory and Physical Interpretation of D = 1 Strings, Mod. Phys. Lett. A 5 (1990) 1639 [INSPIRE].
A. Jevicki, Development in 2-D string theory, in Workshop on String Theory, Gauge Theory and Quantum Gravity, (1993), DOI [hep-th/9309115] [INSPIRE].
J. Polchinski, Classical limit of (1 + 1)-dimensional string theory, Nucl. Phys. B 362 (1991) 125 [INSPIRE].
S. Alexandrov, Backgrounds of 2-D string theory from matrix model, hep-th/0303190 [INSPIRE].
A. Jevicki and B. Sakita, The Quantum Collective Field Method and Its Application to the Planar Limit, Nucl. Phys. B 165 (1980) 511 [INSPIRE].
A.B. Zamolodchikov and A.B. Zamolodchikov, Liouville field theory on a pseudosphere, hep-th/0101152 [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: 2108.12096
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
Suzuki, K., Takayanagi, T. JT gravity limit of Liouville CFT and matrix model. J. High Energ. Phys. 2021, 137 (2021). https://doi.org/10.1007/JHEP11(2021)137
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2021)137