Abstract
We present an explicit reconstruction of the interior of an AdS2 black hole in Jackiw-Teitelboim gravity, that is entirely formulated in the dual SYK model and makes no direct reference to the gravitational bulk. We do this by introducing a probe “observer” in the right wormhole exterior and using the prescription of [arXiv:2009.04476] to transport SYK operators along the probe’s infalling worldline and into the black hole interior, using an appropriate SYK modular Hamiltonian. Our SYK computation recovers the precise proper time at which signals sent from the left boundary are registered by our observer’s apparatus inside the wormhole. The success of the computation relies on the universal properties of SYK and we outline a promising avenue for extending it to higher dimensions and applying it to the computation of scattering amplitudes behind the horizon.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
D.L. Jafferis and L. Lamprou, Inside the hologram: reconstructing the bulk observer’s experience, JHEP 03 (2022) 084 [arXiv:2009.04476] [INSPIRE].
B. Yoshida, Firewalls vs. Scrambling, JHEP 10 (2019) 132 [arXiv:1902.09763] [INSPIRE].
B. Yoshida, Observer-dependent black hole interior from operator collision, Phys. Rev. D 103 (2021) 046004 [arXiv:1910.11346] [INSPIRE].
J. de Boer, D.L. Jafferis and L. Lamprou, Inside holographic black holes: Melting the frozen vacuum, to appear.
S. Sachdev, Holographic metals and the fractionalized Fermi liquid, Phys. Rev. Lett. 105 (2010) 151602 [arXiv:1006.3794] [INSPIRE].
S. Sachdev and J. Ye, Gapless spin fluid ground state in a random, quantum Heisenberg magnet, Phys. Rev. Lett. 70 (1993) 3339 [cond-mat/9212030] [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].
D. Stanford, More quantum noise from wormholes, arXiv:2008.08570 [INSPIRE].
J. Maldacena and L. Susskind, Cool horizons for entangled black holes, Fortsch. Phys. 61 (2013) 781 [arXiv:1306.0533] [INSPIRE].
J. Maldacena, D. Stanford and Z. Yang, Diving into traversable wormholes, Fortsch. Phys. 65 (2017) 1700034 [arXiv:1704.05333] [INSPIRE].
D.A. Roberts, D. Stanford and A. Streicher, Operator growth in the SYK model, JHEP 06 (2018) 122 [arXiv:1802.02633] [INSPIRE].
X.-L. Qi and A. Streicher, Quantum Epidemiology: Operator Growth, Thermal Effects, and SYK, JHEP 08 (2019) 012 [arXiv:1810.11958] [INSPIRE].
S. Nezami, H.W. Lin, A.R. Brown, H. Gharibyan, S. Leichenauer, G. Salton et al., Quantum Gravity in the Lab: Teleportation by Size and Traversable Wormholes, Part II, arXiv:2102.01064 [INSPIRE].
F.M. Haehl and Y. Zhao, Size and momentum of an infalling particle in the black hole interior, JHEP 06 (2021) 056 [arXiv:2102.05697] [INSPIRE].
S.-K. Jian, B. Swingle and Z.-Y. Xian, Complexity growth of operators in the SYK model and in JT gravity, JHEP 03 (2021) 014 [arXiv:2008.12274] [INSPIRE].
Y.D. Lensky, X.-L. Qi and P. Zhang, Size of bulk fermions in the SYK model, JHEP 10 (2020) 053 [arXiv:2002.01961] [INSPIRE].
P. Gao and D.L. Jafferis, A traversable wormhole teleportation protocol in the SYK model, JHEP 07 (2021) 097 [arXiv:1911.07416] [INSPIRE].
A. Lucas, Operator size at finite temperature and Planckian bounds on quantum dynamics, Phys. Rev. Lett. 122 (2019) 216601 [arXiv:1809.07769] [INSPIRE].
T. Schuster, B. Kobrin, P. Gao, I. Cong, E.T. Khabiboulline, N.M. Linke et al., Many-body quantum teleportation via operator spreading in the traversable wormhole protocol, arXiv:2102.00010 [INSPIRE].
J. Maldacena and X.-L. Qi, Eternal traversable wormhole, arXiv:1804.00491 [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. Gao, D.L. Jafferis and D.K. Kolchmeyer, An effective matrix model for dynamical end of the world branes in Jackiw-Teitelboim gravity, JHEP 01 (2022) 038 [arXiv:2104.01184] [INSPIRE].
P. Saad, S.H. Shenker and D. Stanford, JT gravity as a matrix integral, arXiv:1903.11115 [INSPIRE].
N. Engelhardt, S. Fischetti and A. Maloney, Free energy from replica wormholes, Phys. Rev. D 103 (2021) 046021 [arXiv:2007.07444] [INSPIRE].
P. Saad, S.H. Shenker and D. Stanford, A semiclassical ramp in SYK and in gravity, arXiv:1806.06840 [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].
A. Hamilton, D.N. Kabat, G. Lifschytz and D.A. Lowe, Holographic representation of local bulk operators, Phys. Rev. D 74 (2006) 066009 [hep-th/0606141] [INSPIRE].
A. Hamilton, D.N. Kabat, G. Lifschytz and D.A. Lowe, Local bulk operators in AdS/CFT: A Holographic description of the black hole interior, Phys. Rev. D 75 (2007) 106001 [Erratum ibid. 75 (2007) 129902] [hep-th/0612053] [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].
P. Gao and H. Liu, Regenesis and quantum traversable wormholes, JHEP 10 (2019) 048 [arXiv:1810.01444] [INSPIRE].
H.W. Lin, J. Maldacena and Y. Zhao, Symmetries Near the Horizon, JHEP 08 (2019) 049 [arXiv:1904.12820] [INSPIRE].
V. Chandrasekaran, T. Faulkner and A. Levine, Scattering strings off quantum extremal surfaces, arXiv:2108.01093 [INSPIRE].
I. Kourkoulou and J. Maldacena, Pure states in the SYK model and nearly-AdS2 gravity, arXiv:1707.02325 [INSPIRE].
J. De Boer, R. Van Breukelen, S.F. Lokhande, K. Papadodimas and E. Verlinde, Probing typical black hole microstates, JHEP 01 (2020) 062 [arXiv:1901.08527] [INSPIRE].
R. Brustein and Y. Zigdon, Revealing the interior of black holes out of equilibrium in the Sachdev-Ye-Kitaev model, Phys. Rev. D 98 (2018) 066013 [arXiv:1804.09017] [INSPIRE].
S. Leutheusser and H. Liu, Causal connectability between quantum systems and the black hole interior in holographic duality, arXiv:2110.05497 [INSPIRE].
A. Bouland, B. Fefferman and U. Vazirani, Computational pseudorandomness, the wormhole growth paradox, and constraints on the AdS/CFT duality, arXiv:1910.14646 [INSPIRE].
M. Blake and H. Liu, On systems of maximal quantum chaos, JHEP 05 (2021) 229 [arXiv:2102.11294] [INSPIRE].
M. Blake, H. Lee and H. Liu, A quantum hydrodynamical description for scrambling and many-body chaos, JHEP 10 (2018) 127 [arXiv:1801.00010] [INSPIRE].
L. D’Alessio, Y. Kafri, A. Polkovnikov and M. Rigol, From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics, Adv. Phys. 65 (2016) 239 [arXiv:1509.06411] [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].
A. Belin and J. de Boer, Random statistics of OPE coefficients and Euclidean wormholes, Class. Quant. Grav. 38 (2021) 164001 [arXiv:2006.05499] [INSPIRE].
A. Belin, J. de Boer and D. Liska, Non-Gaussianities in the Statistical Distribution of Heavy OPE Coefficients and Wormholes, arXiv:2110.14649 [INSPIRE].
L. Foini and J. Kurchan, Eigenstate thermalization hypothesis and out of time order correlators, Phys. Rev. E 99 (2019) 042139 [arXiv:1803.10658] [INSPIRE].
F.M. Haehl, A. Streicher and Y. Zhao, Six-point functions and collisions in the black hole interior, JHEP 08 (2021) 134 [arXiv:2105.12755] [INSPIRE].
S.H. Shenker and D. Stanford, Black holes and the butterfly effect, JHEP 03 (2014) 067 [arXiv:1306.0622] [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].
A.R. Brown, H. Gharibyan, G. Penington and L. Susskind, The Python’s Lunch: geometric obstructions to decoding Hawking radiation, JHEP 08 (2020) 121 [arXiv:1912.00228] [INSPIRE].
D. Harlow and D. Jafferis, The Factorization Problem in Jackiw-Teitelboim Gravity, JHEP 02 (2020) 177 [arXiv:1804.01081] [INSPIRE].
C. Choi, M. Mezei and G. Sárosi, Pole skipping away from maximal chaos, arXiv:2010.08558 [INSPIRE].
G. Sárosi, AdS2 holography and the SYK model, PoS Modave2017 (2018) 001 [arXiv:1711.08482] [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: 2111.14010
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
Gao, P., Lamprou, L. Seeing behind black hole horizons in SYK. J. High Energ. Phys. 2022, 143 (2022). https://doi.org/10.1007/JHEP06(2022)143
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP06(2022)143