Abstract
The black hole interior is a mysterious region of spacetime where non-perturbative effects are sometimes important. These non-perturbative effects are believed to be highly theory-dependent. We sharpen these statements by considering a setup where the state of the black hole is in a superposition of states corresponding to boundary theories with different couplings, entangled with a reference which keeps track of those couplings. The entanglement wedge of the reference can then be interpreted as the bulk region most sensitive to the values of the couplings. In simple bulk models, e.g., JT gravity + a matter BCFT, the QES formula implies that the reference contains the black hole interior at late times. We also analyze the Renyi-2 entropy tr ρ2 of the reference, which can be viewed as a diagnostic of chaos via the Loschmidt echo. We find explicitly the replica wormhole that diagnoses the island and restores unitarity. Numerical and analytical evidence of these statements in the SYK model is presented. Similar considerations are expected to apply in higher dimensional AdS/CFT, for marginal and even irrelevant couplings.
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References
G. Penington, Entanglement Wedge Reconstruction and the Information Paradox, JHEP 09 (2020) 002 [arXiv:1905.08255] [INSPIRE].
A. Almheiri, N. Engelhardt, D. Marolf and H. Maxfield, The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole, JHEP 12 (2019) 063 [arXiv:1905.08762] [INSPIRE].
J.S. Cotler et al., Black Holes and Random Matrices, JHEP 05 (2017) 118 [Erratum ibid. 09 (2018) 002] [arXiv:1611.04650] [INSPIRE].
P. Saad, S.H. Shenker and D. Stanford, A semiclassical ramp in SYK and in gravity, arXiv:1806.06840 [INSPIRE].
J. Polchinski, Chaos in the black hole S-matrix, arXiv:1505.08108 [INSPIRE].
P. Saad, S.H. Shenker, D. Stanford and S. Yao, Wormholes without averaging, arXiv:2103.16754 [INSPIRE].
X.-L. Qi, Z. Shangnan and Z. Yang, Holevo information and ensemble theory of gravity, JHEP 02 (2022) 056 [arXiv:2111.05355] [INSPIRE].
R. Renner and J. Wang, The black hole information puzzle and the quantum de Finetti theorem, arXiv:2110.14653 [INSPIRE].
A. Hamilton, D.N. Kabat, G. Lifschytz and D.A. Lowe, Local bulk operators in AdS/CFT: A Boundary view of horizons and locality, Phys. Rev. D 73 (2006) 086003 [hep-th/0506118] [INSPIRE].
D.L. Jafferis, A. Lewkowycz, J. Maldacena and S.J. Suh, Relative entropy equals bulk relative entropy, JHEP 06 (2016) 004 [arXiv:1512.06431] [INSPIRE].
X. Dong, D. Harlow and A.C. Wall, Reconstruction of Bulk Operators within the Entanglement Wedge in Gauge-Gravity Duality, Phys. Rev. Lett. 117 (2016) 021601 [arXiv:1601.05416] [INSPIRE].
X.-L. Qi, Entanglement island, miracle operators and the firewall, JHEP 01 (2022) 085 [arXiv:2105.06579] [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].
T. Faulkner, A. Lewkowycz and J. Maldacena, Quantum corrections to holographic entanglement entropy, JHEP 11 (2013) 074 [arXiv:1307.2892] [INSPIRE].
N. Engelhardt and A.C. Wall, Quantum Extremal Surfaces: Holographic Entanglement Entropy beyond the Classical Regime, JHEP 01 (2015) 073 [arXiv:1408.3203] [INSPIRE].
P. Saad, S.H. Shenker and D. Stanford, JT gravity as a matrix integral, arXiv:1903.11115 [INSPIRE].
J. Maldacena and D. Stanford, Remarks on the Sachdev-Ye-Kitaev model, Phys. Rev. D 94 (2016) 106002 [arXiv:1604.07818] [INSPIRE].
J.L. Cardy, Boundary conformal field theory, hep-th/0411189 [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].
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].
P. Saad, Late Time Correlation Functions, Baby Universes, and ETH in JT Gravity, arXiv:1910.10311 [INSPIRE].
Z. Yang, The Quantum Gravity Dynamics of Near Extremal Black Holes, JHEP 05 (2019) 205 [arXiv:1809.08647] [INSPIRE].
J. Maldacena and X.-L. Qi, Eternal traversable wormhole, arXiv:1804.00491 [INSPIRE].
D. Stanford, More quantum noise from wormholes, arXiv:2008.08570 [INSPIRE].
X.-L. Qi and A. Streicher, Quantum Epidemiology: Operator Growth, Thermal Effects, and SYK, JHEP 08 (2019) 012 [arXiv:1810.11958] [INSPIRE].
A. Streicher, SYK Correlators for All Energies, JHEP 02 (2020) 048 [arXiv:1911.10171] [INSPIRE].
A. Eberlein, V. Kasper, S. Sachdev and J. Steinberg, Quantum quench of the Sachdev-Ye-Kitaev Model, Phys. Rev. B 96 (2017) 205123 [arXiv:1706.07803] [INSPIRE].
A. Goel, H.T. Lam, G.J. Turiaci and H. Verlinde, Expanding the Black Hole Interior: Partially Entangled Thermal States in SYK, JHEP 02 (2019) 156 [arXiv:1807.03916] [INSPIRE].
G. Penington, S.H. Shenker, D. Stanford and Z. Yang, Replica wormholes and the black hole interior, JHEP 03 (2022) 205 [arXiv:1911.11977] [INSPIRE].
A. Almheiri, D. Marolf, J. Polchinski and J. Sully, Black Holes: Complementarity or Firewalls?, JHEP 02 (2013) 062 [arXiv:1207.3123] [INSPIRE].
A. Almheiri, D. Marolf, J. Polchinski, D. Stanford and J. Sully, An Apologia for Firewalls, JHEP 09 (2013) 018 [arXiv:1304.6483] [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].
A. Almheiri, R. Mahajan and J. Maldacena, Islands outside the horizon, arXiv:1910.11077 [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].
R. Bousso and M. Tomašević, Unitarity From a Smooth Horizon?, Phys. Rev. D 102 (2020) 106019 [arXiv:1911.06305] [INSPIRE].
R. Bousso and E. Wildenhain, Gravity/ensemble duality, Phys. Rev. D 102 (2020) 066005 [arXiv:2006.16289] [INSPIRE].
J.M. Maldacena, Eternal black holes in anti-de Sitter, JHEP 04 (2003) 021 [hep-th/0106112] [INSPIRE].
H.W. Lin, J. Maldacena and Y. Zhao, Symmetries Near the Horizon, JHEP 08 (2019) 049 [arXiv:1904.12820] [INSPIRE].
J. Maldacena, S.H. Shenker and D. Stanford, A bound on chaos, JHEP 08 (2016) 106 [arXiv:1503.01409] [INSPIRE].
R. Penrose, Gravitational collapse: The role of general relativity, Riv. Nuovo Cim. 1 (1969) 252 [INSPIRE].
D. Bak, M. Gutperle and S. Hirano, A Dilatonic deformation of AdS5 and its field theory dual, JHEP 05 (2003) 072 [hep-th/0304129] [INSPIRE].
A.B. Clark, D.Z. Freedman, A. Karch and M. Schnabl, Dual of the Janus solution: An interface conformal field theory, Phys. Rev. D 71 (2005) 066003 [hep-th/0407073] [INSPIRE].
A. Clark and A. Karch, Super Janus, JHEP 10 (2005) 094 [hep-th/0506265] [INSPIRE].
D. Gaiotto and E. Witten, Janus Configurations, Chern-Simons Couplings, And The theta-Angle in \( \mathcal{N} \) = 4 Super Yang-Mills Theory, JHEP 06 (2010) 097 [arXiv:0804.2907] [INSPIRE].
D. Bak, M. Gutperle and S. Hirano, Three dimensional Janus and time-dependent black holes, JHEP 02 (2007) 068 [hep-th/0701108] [INSPIRE].
C. Bachas and V. Papadopoulos, Phases of Holographic Interfaces, JHEP 04 (2021) 262 [arXiv:2101.12529] [INSPIRE].
P. Simidzija and M. Van Raamsdonk, Holo-ween, JHEP 12 (2020) 028 [arXiv:2006.13943] [INSPIRE].
A. May, P. Simidzija and M. Van Raamsdonk, Negative energy enhancement in layered holographic conformal field theories, JHEP 08 (2021) 037 [arXiv:2103.14046] [INSPIRE].
M. Oshikawa and I. Affleck, Boundary conformal field theory approach to the critical two-dimensional Ising model with a defect line, Nucl. Phys. B 495 (1997) 533 [cond-mat/9612187] [INSPIRE].
D. Stanford and E. Witten, Fermionic Localization of the Schwarzian Theory, JHEP 10 (2017) 008 [arXiv:1703.04612] [INSPIRE].
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Almheiri, A., Lin, H.W. The entanglement wedge of unknown couplings. J. High Energ. Phys. 2022, 62 (2022). https://doi.org/10.1007/JHEP08(2022)062
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DOI: https://doi.org/10.1007/JHEP08(2022)062