Abstract
We study further the duality between semiclassical AdS3 and formal CFT2 ensembles. First, we study torus wormholes (Maldacena-Maoz wormholes with two torus boundaries) with one insertion or two insertions on each boundary and find that they give non-decaying contribution to the product of two torus one-point or two-point functions at late-time. Second, we study the ℤ2 quotients of a torus wormhole such that the outcome has one boundary. We identify quotients that give non-decaying contributions to the torus two-point function at late-time.
We comment on reflection (R) or time-reversal (T) symmetry vs. the combination RT that is a symmetry of any relativistic field theory. RT symmetry itself implies that to the extent that a relativistic quantum field theory exhibits random matrix statistics it should be of the GOE type for bosonic states and of the GSE type for fermionic states. We discuss related implications of these symmetries for wormholes.
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References
J. Chandra, S. Collier, T. Hartman and A. Maloney, Semiclassical 3D gravity as an average of large-c CFTs, JHEP 12 (2022) 069 [arXiv:2203.06511] [INSPIRE].
A. Belin and J. de Boer, Random statistics of OPE coefficients and Euclidean wormholes, Class. Quant. Grav. 38 (2021) 164001 [arXiv:2006.05499] [INSPIRE].
S. Collier, A. Maloney, H. Maxfield and I. Tsiares, Universal dynamics of heavy operators in CFT2, JHEP 07 (2020) 074 [arXiv:1912.00222] [INSPIRE].
J. Cotler and K. Jensen, AdS3 gravity and random CFT, JHEP 04 (2021) 033 [arXiv:2006.08648] [INSPIRE].
A. Maloney and E. Witten, Averaging over Narain moduli space, JHEP 10 (2020) 187 [arXiv:2006.04855] [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].
C. Teitelboim, Gravitation and Hamiltonian Structure in Two Space-Time Dimensions, Phys. Lett. B 126 (1983) 41 [INSPIRE].
R. Jackiw, Lower Dimensional Gravity, Nucl. Phys. B 252 (1985) 343 [INSPIRE].
A. Almheiri and J. Polchinski, Models of AdS2 backreaction and holography, JHEP 11 (2015) 014 [arXiv:1402.6334] [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].
M. Srednicki, Chaos and Quantum Thermalization, cond-mat/9403051 [https://doi.org/10.1103/PhysRevE.50.888] [INSPIRE].
J. Deutsch, Quantum statistical mechanics in a closed system, Phys. Rev. A 43 (1991) 2046.
M. Banados, C. Teitelboim and J. Zanelli, The Black hole in three-dimensional space-time, Phys. Rev. Lett. 69 (1992) 1849 [hep-th/9204099] [INSPIRE].
J.M. Maldacena and L. Maoz, Wormholes in AdS, JHEP 02 (2004) 053 [hep-th/0401024] [INSPIRE].
J. Cotler and K. Jensen, AdS3 wormholes from a modular bootstrap, JHEP 11 (2020) 058 [arXiv:2007.15653] [INSPIRE].
A. Maloney and E. Witten, Quantum Gravity Partition Functions in Three Dimensions, JHEP 02 (2010) 029 [arXiv:0712.0155] [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].
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].
C. Yan, Crosscap Contribution to Late-Time Two-Point Correlators, arXiv:2203.14436 [INSPIRE].
S. Collier, L. Eberhardt and M. Zhang, Solving 3d Gravity with Virasoro TQFT, SciPost Phys. 15 (2023) 151 [arXiv:2304.13650] [INSPIRE].
P. Saad, S.H. Shenker and D. Stanford, A semiclassical ramp in SYK and in gravity, arXiv:1806.06840 [INSPIRE].
F.J. Dyson, Statistical theory of the energy levels of complex systems. Part I, J. Math. Phys. 3 (1962) 140 [INSPIRE].
D. Stanford, Z. Yang and S. Yao, Subleading Weingartens, JHEP 02 (2022) 200 [arXiv:2107.10252] [INSPIRE].
E. Witten, Fermion Path Integrals And Topological Phases, Rev. Mod. Phys. 88 (2016) 035001 [arXiv:1508.04715] [INSPIRE].
P. Saad, Late Time Correlation Functions, Baby Universes, and ETH in JT Gravity, arXiv:1910.10311 [INSPIRE].
A. Blommaert, T.G. Mertens and H. Verschelde, Clocks and Rods in Jackiw-Teitelboim Quantum Gravity, JHEP 09 (2019) 060 [arXiv:1902.11194] [INSPIRE].
Z. Yang, The Quantum Gravity Dynamics of Near Extremal Black Holes, JHEP 05 (2019) 205 [arXiv:1809.08647] [INSPIRE].
H.T. Lam, T.G. Mertens, G.J. Turiaci and H. Verlinde, Shockwave S-matrix from Schwarzian Quantum Mechanics, JHEP 11 (2018) 182 [arXiv:1804.09834] [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].
A. Blommaert, T.G. Mertens and H. Verschelde, The Schwarzian Theory — A Wilson Line Perspective, JHEP 12 (2018) 022 [arXiv:1806.07765] [INSPIRE].
L.V. Iliesiu, S.S. Pufu, H. Verlinde and Y. Wang, An exact quantization of Jackiw-Teitelboim gravity, JHEP 11 (2019) 091 [arXiv:1905.02726] [INSPIRE].
J.M. Maldacena, D. Stanford and Z. Yang, Diving into traversable wormholes, Fortsch. Phys. 65 (2017) 1700034 [arXiv:1704.05333] [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].
J.S. Cotler et al., Black Holes and Random Matrices, JHEP 05 (2017) 118 [Erratum ibid. 09 (2018) 002] [arXiv:1611.04650] [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].
D. Stanford and E. Witten, Fermionic Localization of the Schwarzian Theory, JHEP 10 (2017) 008 [arXiv:1703.04612] [INSPIRE].
V.V. Belokurov and E.T. Shavgulidze, Exact solution of the Schwarzian theory, Phys. Rev. D 96 (2017) 101701 [arXiv:1705.02405] [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].
A. Kitaev and S.J. Suh, Statistical mechanics of a two-dimensional black hole, JHEP 05 (2019) 198 [arXiv:1808.07032] [INSPIRE].
Acknowledgments
I want to give special thanks to Douglas Stanford for patient guidance, extensive discussions, and inspiring comments throughout this project. I am also grateful to Eleny Ionel, Steven Kerckhoff, Raghu Mahajan, Henry Maxfield, and Xiaoliang Qi for discussions.
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ArXiv ePrint: 2305.10494v2
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Yan, C. More on torus wormholes in 3d gravity. J. High Energ. Phys. 2023, 39 (2023). https://doi.org/10.1007/JHEP11(2023)039
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DOI: https://doi.org/10.1007/JHEP11(2023)039