Abstract
We investigate a dilaton gravity model in AdS2 proposed by Almheiri and Polchinski [1] and develop a 1d effective description in terms of a dynamical boundary time with a Schwarzian derivative action. We show that the effective model is equivalent to a 1d version of Liouville theory, and investigate its dynamics and symmetries via a standard canonical framework. We include the coupling to arbitrary conformal matter and analyze the effective action in the presence of possible sources. We compute commutators of local operators at large time separation, and match the result with the time shift due to a gravitational shockwave interaction. We study a black hole evaporation process and comment on the role of entropy in this model.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
A. Almheiri and J. Polchinski, Models of AdS 2 backreaction and holography, JHEP 11 (2015) 014 [arXiv:1402.6334] [INSPIRE].
J.M. Maldacena, J. Michelson and A. Strominger, Anti-de Sitter fragmentation, JHEP 02 (1999) 011 [hep-th/9812073] [INSPIRE].
A. Strominger, AdS 2 quantum gravity and string theory, JHEP 01 (1999) 007 [hep-th/9809027] [INSPIRE].
V. Balasubramanian, J. de Boer, M.M. Sheikh-Jabbari and J. Simon, What is a chiral 2d CFT? And what does it have to do with extremal black holes?, JHEP 02 (2010) 017 [arXiv:0906.3272] [INSPIRE].
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].
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].
S.B. Giddings and W.M. Nelson, Quantum emission from two-dimensional black holes, Phys. Rev. D 46 (1992) 2486 [hep-th/9204072] [INSPIRE].
M. Spradlin and A. Strominger, Vacuum states for AdS 2 black holes, JHEP 11 (1999) 021 [hep-th/9904143] [INSPIRE].
A. Fabbri and J. Navarro-Salas, Modeling black hole evaporation, Imperial College Press, London U.K. (2005).
T.D. Chung and H.L. Verlinde, Dynamical moving mirrors and black holes, Nucl. Phys. B 418 (1994) 305 [hep-th/9311007] [INSPIRE].
K. Schoutens, H.L. Verlinde and E.P. Verlinde, Black hole evaporation and quantum gravity, in Proceedings of International Conference on Strings 93, Berkeley U.S.A. (1993), and in Workshop on String Theory, Gauge Theory and Quantum Gravity, Trieste Italy (1993) [hep-th/9401081] [INSPIRE].
S. Sachdev and J.-w. 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 — 2015, at KITP Program: Entanglement in Strongly-Correlated Quantum Matter, Santa Barbara U.S.A. (2015), http://online.kitp.ucsb.edu/online/entangled15/.
S. Sachdev, Bekenstein-Hawking Entropy and Strange Metals, Phys. Rev. X 5 (2015) 041025 [arXiv:1506.05111] [INSPIRE].
J. Polchinski and V. Rosenhaus, The Spectrum in the Sachdev-Ye-Kitaev Model, JHEP 04 (2016) 001 [arXiv:1601.06768] [INSPIRE].
A. Jevicki, K. Suzuki and J. Yoon, Bi-Local Holography in the SYK Model, JHEP 07 (2016) 007 [arXiv:1603.06246] [INSPIRE].
J. Maldacena and D. Stanford, Comments on the Sachdev-Ye-Kitaev model, arXiv:1604.07818 [INSPIRE].
S. Sachdev, Holographic metals and the fractionalized Fermi liquid, Phys. Rev. Lett. 105 (2010) 151602 [arXiv:1006.3794] [INSPIRE].
T. Dray and G. ’t Hooft, The Gravitational Shock Wave of a Massless Particle, Nucl. Phys. B 253 (1985) 173 [INSPIRE].
S.H. Shenker and D. Stanford, Black holes and the butterfly effect, JHEP 03 (2014) 067 [arXiv:1306.0622] [INSPIRE].
S.H. Shenker and D. Stanford, Multiple Shocks, JHEP 12 (2014) 046 [arXiv:1312.3296] [INSPIRE].
S. Jackson, L. McGough and H. Verlinde, Conformal Bootstrap, Universality and Gravitational Scattering, Nucl. Phys. B 901 (2015) 382 [arXiv:1412.5205] [INSPIRE].
G. Turiaci and H. Verlinde, On CFT and Quantum Chaos, arXiv:1603.03020 [INSPIRE].
J. Polchinski, Chaos in the black hole S-matrix, arXiv:1505.08108 [INSPIRE].
J. Maldacena, S.H. Shenker and D. Stanford, A bound on chaos, arXiv:1503.01409 [INSPIRE].
K. Jensen, Chaos and hydrodynamics near AdS 2, arXiv:1605.06098 [INSPIRE].
J. Maldacena, D. Stanford and Z. Yang, Conformal symmetry and its breaking in two dimensional Nearly Anti-de-Sitter space, arXiv:1606.01857 [INSPIRE].
G.L. Pimentel, A.M. Polyakov and G.M. Tarnopolsky, Vacuum decay in CFT and the Riemann-Hilbert problem, Nucl. Phys. B 907 (2016) 617 [arXiv:1512.06721] [INSPIRE].
S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001] [INSPIRE].
J. de Boer, M.P. Heller, R.C. Myers and Y. Neiman, Holographic de Sitter Geometry from Entanglement in Conformal Field Theory, Phys. Rev. Lett. 116 (2016) 061602 [arXiv:1509.00113] [INSPIRE].
C.T. Asplund, N. Callebaut and C. Zukowski, Equivalence of Emergent de Sitter Spaces from Conformal Field Theory, arXiv:1604.02687 [INSPIRE].
V. Balasubramanian and P. Kraus, A Stress tensor for Anti-de Sitter gravity, Commun. Math. Phys. 208 (1999) 413 [hep-th/9902121] [INSPIRE].
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1606.03438
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Engelsöy, J., Mertens, T.G. & Verlinde, H. An investigation of AdS2 backreaction and holography. J. High Energ. Phys. 2016, 139 (2016). https://doi.org/10.1007/JHEP07(2016)139
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP07(2016)139