Abstract
We study \( \hat{\mathrm{CGHS}} \) gravity, a variant of the matterless Callan-Giddings-Harvey-Strominger model. We show that it describes a universal sector of the near horizon perturbations of non-extremal black holes in higher dimensions. In many respects this theory can be viewed as a flat space analog of Jackiw-Teitelboim gravity. The result for the Euclidean path integral implies that \( \hat{\mathrm{CGHS}} \) is dual to a Gaussian ensemble that we describe in detail. The simplicity of this theory allows us to compute exact quantities such as the quenched free energy and provides a useful playground to study baby universes, averages and factorization. In particular we derive a “wormhole = diagonal” identity. We also give evidence for the existence of a non-perturbative completion in terms of a matrix model. Finally, flat wormhole solutions in this model are discussed.
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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].
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].
P. Saad, S.H. Shenker and D. Stanford, JT gravity as a matrix integral, arXiv:1903.11115 [INSPIRE].
H. Afshar, H.A. González, D. Grumiller and D. Vassilevich, Flat space holography and the complex Sachdev-Ye-Kitaev model, Phys. Rev. D 101 (2020) 086024 [arXiv:1911.05739] [INSPIRE].
A. Strominger and C. Vafa, Microscopic origin of the Bekenstein-Hawking entropy, Phys. Lett. B 379 (1996) 99 [hep-th/9601029] [INSPIRE].
A. Strominger, Black hole entropy from near horizon microstates, JHEP 02 (1998) 009 [hep-th/9712251] [INSPIRE].
A. Sen, Black Hole Entropy Function, Attractors and Precision Counting of Microstates, Gen. Rel. Grav. 40 (2008) 2249 [arXiv:0708.1270] [INSPIRE].
J.M. Maldacena, J. Michelson and A. Strominger, Anti-de Sitter fragmentation, JHEP 02 (1999) 011 [hep-th/9812073] [INSPIRE].
A. Sen, Quantum Entropy Function from AdS2/CFT1 Correspondence, Int. J. Mod. Phys. A 24 (2009) 4225 [arXiv:0809.3304] [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. Engelsöy, T.G. Mertens and H. Verlinde, An investigation of AdS2 backreaction and holography, JHEP 07 (2016) 139 [arXiv:1606.03438] [INSPIRE].
A. Almheiri, T. Hartman, J. Maldacena, E. Shaghoulian and A. Tajdini, The entropy of Hawking radiation, arXiv:2006.06872 [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].
A. Kitaev, A simple model of quantum holography (part 1), talk at KITP, April 7, 2015, http://online.kitp.ucsb.edu/online/entangled15/kitaev/.
A. Kitaev, A simple model of quantum holography (part 2), talk at KITP, May 27, 2015, http://online.kitp.ucsb.edu/online/entangled15/kitaev2/.
J. Maldacena and D. Stanford, Remarks on the Sachdev-Ye-Kitaev model, Phys. Rev. D 94 (2016) 106002 [arXiv:1604.07818] [INSPIRE].
A. Almheiri and B. Kang, Conformal Symmetry Breaking and Thermodynamics of Near-Extremal Black Holes, JHEP 10 (2016) 052 [arXiv:1606.04108] [INSPIRE].
P. Nayak, A. Shukla, R.M. Soni, S.P. Trivedi and V. Vishal, On the Dynamics of Near-Extremal Black Holes, JHEP 09 (2018) 048 [arXiv:1802.09547] [INSPIRE].
U. Moitra, S.K. Sake, S.P. Trivedi and V. Vishal, Jackiw-Teitelboim Gravity and Rotating Black Holes, JHEP 11 (2019) 047 [arXiv:1905.10378] [INSPIRE].
D. Anninos, T. Anous and R.T. D’Agnolo, Marginal deformations & rotating horizons, JHEP 12 (2017) 095 [arXiv:1707.03380] [INSPIRE].
A. Castro, F. Larsen and I. Papadimitriou, 5D rotating black holes and the nAdS2/nCFT1 correspondence, JHEP 10 (2018) 042 [arXiv:1807.06988] [INSPIRE].
A. Castro and V. Godet, Breaking away from the near horizon of extreme Kerr, SciPost Phys. 8 (2020) 089 [arXiv:1906.09083] [INSPIRE].
A. Castro, V. Godet, J. Simón, W. Song and B. Yu, Gravitational perturbations from NHEK to Kerr, arXiv:2102.08060 [INSPIRE].
L.V. Iliesiu and G.J. Turiaci, The statistical mechanics of near-extremal black holes, JHEP 05 (2021) 145 [arXiv:2003.02860] [INSPIRE].
M. Heydeman, L.V. Iliesiu, G.J. Turiaci and W. Zhao, The statistical mechanics of near-BPS black holes, arXiv:2011.01953 [INSPIRE].
G.V. Lavrelashvili, V.A. Rubakov and P.G. Tinyakov, Disruption of Quantum Coherence upon a Change in Spatial Topology in Quantum Gravity, JETP Lett. 46 (1987) 167 [INSPIRE].
S.W. Hawking, Quantum Coherence Down the Wormhole, Phys. Lett. B 195 (1987) 337 [INSPIRE].
S.B. Giddings and A. Strominger, Axion Induced Topology Change in Quantum Gravity and String Theory, Nucl. Phys. B 306 (1988) 890 [INSPIRE].
S.B. Giddings and A. Strominger, Loss of Incoherence and Determination of Coupling Constants in Quantum Gravity, Nucl. Phys. B 307 (1988) 854 [INSPIRE].
S.B. Giddings and A. Strominger, Baby Universes, Third Quantization and the Cosmological Constant, Nucl. Phys. B 321 (1989) 481 [INSPIRE].
S.R. Coleman, Why There Is Nothing Rather Than Something: A Theory of the Cosmological Constant, Nucl. Phys. B 310 (1988) 643 [INSPIRE].
G.W. Gibbons and S.W. Hawking, Action Integrals and Partition Functions in Quantum Gravity, Phys. Rev. D 15 (1977) 2752 [INSPIRE].
J.M. Maldacena and L. Maoz, Wormholes in AdS, JHEP 02 (2004) 053 [hep-th/0401024] [INSPIRE].
P. Betzios, E. Kiritsis and O. Papadoulaki, Euclidean Wormholes and Holography, JHEP 06 (2019) 042 [arXiv:1903.05658] [INSPIRE].
A. Blommaert, T.G. Mertens and H. Verschelde, Eigenbranes in Jackiw-Teitelboim gravity, JHEP 02 (2021) 168 [arXiv:1911.11603] [INSPIRE].
D. Marolf and H. Maxfield, Transcending the ensemble: baby universes, spacetime wormholes, and the order and disorder of black hole information, JHEP 08 (2020) 044 [arXiv:2002.08950] [INSPIRE].
J. Pollack, M. Rozali, J. Sully and D. Wakeham, Eigenstate Thermalization and Disorder Averaging in Gravity, Phys. Rev. Lett. 125 (2020) 021601 [arXiv:2002.02971] [INSPIRE].
M. Van Raamsdonk, Comments on wormholes, ensembles, and cosmology, arXiv:2008.02259 [INSPIRE].
P. Betzios and O. Papadoulaki, Liouville theory and Matrix models: A Wheeler DeWitt perspective, JHEP 09 (2020) 125 [arXiv:2004.00002] [INSPIRE].
S.B. Giddings and G.J. Turiaci, Wormhole calculus, replicas, and entropies, JHEP 09 (2020) 194 [arXiv:2004.02900] [INSPIRE].
A. Blommaert, Dissecting the ensemble in JT gravity, arXiv:2006.13971 [INSPIRE].
T. Anous, J. Kruthoff and R. Mahajan, Density matrices in quantum gravity, SciPost Phys. 9 (2020) 045 [arXiv:2006.17000] [INSPIRE].
Y. Chen, V. Gorbenko and J. Maldacena, Bra-ket wormholes in gravitational ly prepared states, JHEP 02 (2021) 009 [arXiv:2007.16091] [INSPIRE].
L. Eberhardt, Partition functions of the tensionless string, JHEP 03 (2021) 176 [arXiv:2008.07533] [INSPIRE].
D. Stanford, More quantum noise from wormholes, arXiv:2008.08570 [INSPIRE].
J. McNamara and C. Vafa, Baby Universes, Holography, and the Swampland, arXiv:2004.06738 [INSPIRE].
J. Cotler and K. Jensen, Gravitational Constrained Instantons, arXiv:2010.02241 [INSPIRE].
A.M. García-García and V. Godet, Euclidean wormhole in the Sachdev-Ye-Kitaev model, Phys. Rev. D 103 (2021) 046014 [arXiv:2010.11633] [INSPIRE].
D. Marolf and J.E. Santos, AdS Euclidean wormholes, arXiv:2101.08875 [INSPIRE].
L. Eberhardt, Summing over Geometries in String Theory, JHEP 05 (2021) 233 [arXiv:2102.12355] [INSPIRE].
C.G. Callan, Jr., S.B. Giddings, J.A. Harvey and A. Strominger, Evanescent black holes, Phys. Rev. D 45 (1992) R1005 [hep-th/9111056] [INSPIRE].
V. Godet and C. Marteau, New boundary conditions for AdS2, JHEP 12 (2020) 020 [arXiv:2005.08999] [INSPIRE].
N. Engelhardt, S. Fischetti and A. Maloney, Free energy from replica wormholes, Phys. Rev. D 103 (2021) 046021 [arXiv:2007.07444] [INSPIRE].
B. Freivogel, V. Godet, E. Morvan, J.F. Pedraza and A. Rotundo, Lessons on eternal traversable wormholes in AdS, JHEP 07 (2019) 122 [arXiv:1903.05732] [INSPIRE].
H.R. Afshar, Warped Schwarzian theory, JHEP 02 (2020) 126 [arXiv:1908.08089] [INSPIRE].
J. Maldacena, G.J. Turiaci and Z. Yang, Two dimensional Nearly de Sitter gravity, JHEP 01 (2021) 139 [arXiv:1904.01911] [INSPIRE].
D. Stanford and Z. Yang, Finite-cutoff JT gravity and self-avoiding loops, arXiv:2004.08005 [INSPIRE].
D. Stanford and E. Witten, Fermionic Localization of the Schwarzian Theory, JHEP 10 (2017) 008 [arXiv:1703.04612] [INSPIRE].
R.M. Wald, Black hole entropy is the Noether charge, Phys. Rev. D 48 (1993) R3427 [gr-qc/9307038] [INSPIRE].
V. Iyer and R.M. Wald, Some properties of Noether charge and a proposal for dynamical black hole entropy, Phys. Rev. D 50 (1994) 846 [gr-qc/9403028] [INSPIRE].
P. Saad, Island Hopping 2020: from Wormholes to Averages, Talk given at the workshop on 19/11/2020 [https://www.youtube.com/watch?v=dnevNYCa7C8].
J. Cotler and K. Jensen, AdS3 wormholes from a modular bootstrap, JHEP 11 (2020) 058 [arXiv:2007.15653] [INSPIRE].
J. Cotler and K. Jensen, AdS3 gravity and random CFT, JHEP 04 (2021) 033 [arXiv:2006.08648] [INSPIRE].
J.S. Cotler, G. Gur-Ari, M. Hanada, J. Polchinski, P. Saad, S.H. Shenker et al., Black Holes and Random Matrices, JHEP 05 (2017) 118 [Erratum ibid. 09 (2018) 002] [arXiv:1611.04650] [INSPIRE].
O. Janssen, M. Mirbabayi and P. Zograf, Gravity as an ensemble and the moment problem, JHEP 06 (2021) 184 [arXiv:2103.12078] [INSPIRE].
L.V. Iliesiu, On 2D gauge theories in Jackiw-Teitelboim gravity, arXiv:1909.05253 [INSPIRE].
D. Kapec, R. Mahajan and D. Stanford, Matrix ensembles with global symmetries and ‘t Hooft anomalies from 2d gauge theory, JHEP 04 (2020) 186 [arXiv:1912.12285] [INSPIRE].
work in progress.
J. Maldacena and X.-L. Qi, Eternal traversable wormhole, arXiv:1804.00491 [INSPIRE].
M. Van Raamsdonk, Cosmology from confinement?, arXiv:2102.05057 [INSPIRE].
P. Gao, D.L. Jafferis and A.C. Wall, Traversable Wormholes via a Double Trace Deformation, JHEP 12 (2017) 151 [arXiv:1608.05687] [INSPIRE].
L.H. Ford and T.A. Roman, Averaged energy conditions and quantum inequalities, Phys. Rev. D 51 (1995) 4277 [gr-qc/9410043] [INSPIRE].
N. Engelhardt and G.T. Horowitz, Holographic Consequences of a No Transmission Principle, Phys. Rev. D 93 (2016) 026005 [arXiv:1509.07509] [INSPIRE].
S. Bintanja, R. Espíndola, B. Freivogel and D. Nikolakopoulou, How to Make Traversable Wormholes: Eternal AdS4 Wormholes from Coupled CFT’s, arXiv:2102.06628 [INSPIRE].
A. Belin and J. de Boer, Random Statistics of OPE Coefficients and Euclidean Wormholes, arXiv:2006.05499 [INSPIRE].
L.V. Iliesiu, J. Kruthoff, G.J. Turiaci and H. Verlinde, JT gravity at finite cutoff, SciPost Phys. 9 (2020) 023 [arXiv:2004.07242] [INSPIRE].
S.H. Shenker and D. Stanford, Black holes and the butterfly effect, JHEP 03 (2014) 067 [arXiv:1306.0622] [INSPIRE].
A.M. García-García, Y. Jia, D. Rosa and J.J.M. Verbaarschot, Replica Symmetry Breaking and Phase Transitions in a PT Symmetric Sachdev-Ye-Kitaev Model, arXiv:2102.06630 [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].
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Godet, V., Marteau, C. From black holes to baby universes in CGHS gravity. J. High Energ. Phys. 2021, 138 (2021). https://doi.org/10.1007/JHEP07(2021)138
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DOI: https://doi.org/10.1007/JHEP07(2021)138