Abstract
We extend the use of holography to investigate the scrambling properties of various physical systems. Specifically, we consider: (i) non-conformal backgrounds of black Dp branes, (ii) asymptotically Lifshitz black holes, and (iii) black AdS solutions of Gauss-Bonnet gravity. We use the disruption of the entanglement entropy as a probe of the chaotic features of such systems. Our analysis shows that these theories share the same type of behavior as conformal theories as they undergo chaos; however, in the case of Gauss-Bonnet gravity, we find a stark difference in the evolution of the mutual information for negative Gauss-Bonnet coupling. This may signal an inconsistency of the latter.
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References
S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001] [INSPIRE].
S. Ryu and T. Takayanagi, Aspects of holographic entanglement entropy, JHEP 08 (2006) 045 [hep-th/0605073] [INSPIRE].
V.E. Hubeny, M. Rangamani and T. Takayanagi, A covariant holographic entanglement entropy proposal, JHEP 07 (2007) 062 [arXiv:0705.0016] [INSPIRE].
G.T. Horowitz and V.E. Hubeny, Quasinormal modes of AdS black holes and the approach to thermal equilibrium, Phys. Rev. D 62 (2000) 024027 [hep-th/9909056] [INSPIRE].
V. Balasubramanian et al., Holographic thermalization, Phys. Rev. D 84 (2011) 026010 [arXiv:1103.2683] [INSPIRE].
A. Allais and E. Tonni, Holographic evolution of the mutual information, JHEP 01 (2012) 102 [arXiv:1110.1607] [INSPIRE].
R. Callan, J.-Y. He and M. Headrick, Strong subadditivity and the covariant holographic entanglement entropy formula, JHEP 06 (2012) 081 [arXiv:1204.2309] [INSPIRE].
D. Galante and M. Schvellinger, Thermalization with a chemical potential from AdS spaces, JHEP 07 (2012) 096 [arXiv:1205.1548] [INSPIRE].
E. Caceres and A. Kundu, Holographic thermalization with chemical potential, JHEP 09 (2012) 055 [arXiv:1205.2354] [INSPIRE].
E. Caceres, A. Kundu, J.F. Pedraza and W. Tangarife, Strong subadditivity, null energy condition and charged black holes, JHEP 01 (2014) 084 [arXiv:1304.3398] [INSPIRE].
H. Liu and S.J. Suh, Entanglement tsunami: universal scaling in holographic thermalization, Phys. Rev. Lett. 112 (2014) 011601 [arXiv:1305.7244] [INSPIRE].
H. Liu and S.J. Suh, Entanglement growth during thermalization in holographic systems, Phys. Rev. D 89 (2014) 066012 [arXiv:1311.1200] [INSPIRE].
S. Kundu and J.F. Pedraza, Spread of entanglement for small subsystems in holographic CFTs, arXiv:1602.05934 [INSPIRE].
P. Hayden and J. Preskill, Black holes as mirrors: quantum information in random subsystems, JHEP 09 (2007) 120 [arXiv:0708.4025] [INSPIRE].
Y. Sekino and L. Susskind, Fast scramblers, JHEP 10 (2008) 065 [arXiv:0808.2096] [INSPIRE].
S.H. Shenker and D. Stanford, Black holes and the butterfly effect, JHEP 03 (2014) 067 [arXiv:1306.0622] [INSPIRE].
J.M. Maldacena, Eternal black holes in Anti-de Sitter, JHEP 04 (2003) 021 [hep-th/0106112] [INSPIRE].
I.A. Morrison and M.M. Roberts, Mutual information between thermo-field doubles and disconnected holographic boundaries, JHEP 07 (2013) 081 [arXiv:1211.2887] [INSPIRE].
A. Fraser and H. Swinney, Independent coordinates for strange attractors from mutual information, Phys. Rev. A 33 (1986) 1134.
P. Caputa, J. Simón, A. Štikonas, T. Takayanagi and K. Watanabe, Scrambling time from local perturbations of the eternal BTZ black hole, JHEP 08 (2015) 011 [arXiv:1503.08161] [INSPIRE].
P. Hosur, X.-L. Qi, D.A. Roberts and B. Yoshida, Chaos in quantum channels, JHEP 02 (2016) 004 [arXiv:1511.04021] [INSPIRE].
S. Leichenauer, Disrupting entanglement of black holes, Phys. Rev. D 90 (2014) 046009 [arXiv:1405.7365] [INSPIRE].
S.H. Shenker and D. Stanford, Multiple shocks, JHEP 12 (2014) 046 [arXiv:1312.3296] [INSPIRE].
D.A. Roberts, D. Stanford and L. Susskind, Localized shocks, JHEP 03 (2015) 051 [arXiv:1409.8180] [INSPIRE].
S.H. Shenker and D. Stanford, Stringy effects in scrambling, JHEP 05 (2015) 132 [arXiv:1412.6087] [INSPIRE].
J. Maldacena, S.H. Shenker and D. Stanford, A bound on chaos, arXiv:1503.01409 [INSPIRE].
S. Kalyana Rama and B. Sathiapalan, On the role of chaos in the AdS/CFT connection, Mod. Phys. Lett. A 14 (1999) 2635 [hep-th/9905219] [INSPIRE].
N. Itzhaki, J.M. Maldacena, J. Sonnenschein and S. Yankielowicz, Supergravity and the large-N limit of theories with sixteen supercharges, Phys. Rev. D 58 (1998) 046004 [hep-th/9802042] [INSPIRE].
K. Balasubramanian and J. McGreevy, An Analytic Lifshitz black hole, Phys. Rev. D 80 (2009) 104039 [arXiv:0909.0263] [INSPIRE].
R.-G. Cai, Gauss-Bonnet black holes in AdS spaces, Phys. Rev. D 65 (2002) 084014 [hep-th/0109133] [INSPIRE].
R.C. Myers and B. Robinson, Black holes in quasi-topological gravity, JHEP 08 (2010) 067 [arXiv:1003.5357] [INSPIRE].
J. de Boer, M. Kulaxizi and A. Parnachev, Holographic entanglement entropy in Lovelock gravities, JHEP 07 (2011) 109 [arXiv:1101.5781] [INSPIRE].
L.-Y. Hung, R.C. Myers and M. Smolkin, On holographic entanglement entropy and higher curvature gravity, JHEP 04 (2011) 025 [arXiv:1101.5813] [INSPIRE].
R.C. Myers and A. Singh, Comments on holographic entanglement entropy and RG flows, JHEP 04 (2012) 122 [arXiv:1202.2068] [INSPIRE].
J.L.F. Barbon and C.A. Fuertes, A note on the extensivity of the holographic entanglement entropy, JHEP 05 (2008) 053 [arXiv:0801.2153] [INSPIRE].
U. Kol, C. Núñez, D. Schofield, J. Sonnenschein and M. Warschawski, Confinement, phase transitions and non-locality in the entanglement entropy, JHEP 06 (2014) 005 [arXiv:1403.2721] [INSPIRE].
M. Brigante, H. Liu, R.C. Myers, S. Shenker and S. Yaida, The viscosity bound and causality violation, Phys. Rev. Lett. 100 (2008) 191601 [arXiv:0802.3318] [INSPIRE].
E. Caceres, M. Sanchez and J. Virrueta, Holographic entanglement entropy in time dependent Gauss-Bonnet gravity, arXiv:1512.05666 [INSPIRE].
X.O. Camanho, J.D. Edelstein, J. Maldacena and A. Zhiboedov, Causality constraints on corrections to the graviton three-point coupling, JHEP 02 (2016) 020 [arXiv:1407.5597] [INSPIRE].
I.R. Klebanov, D. Kutasov and A. Murugan, Entanglement as a probe of confinement, Nucl. Phys. B 796 (2008) 274 [arXiv:0709.2140] [INSPIRE].
I. Bah, A. Faraggi, L.A. Pando Zayas and C.A. Terrero-Escalante, Holographic entanglement entropy and phase transitions at finite temperature, Int. J. Mod. Phys. A 24 (2009) 2703 [arXiv:0710.5483] [INSPIRE].
A. van Niekerk, Entanglement entropy in non-conformal holographic theories, arXiv:1108.2294 [INSPIRE].
S. Kachru, X. Liu and M. Mulligan, Gravity duals of Lifshitz-like fixed points, Phys. Rev. D 78 (2008) 106005 [arXiv:0808.1725] [INSPIRE].
V. Keranen, E. Keski-Vakkuri and L. Thorlacius, Thermalization and entanglement following a non-relativistic holographic quench, Phys. Rev. D 85 (2012) 026005 [arXiv:1110.5035] [INSPIRE].
H.J. Boonstra, K. Skenderis and P.K. Townsend, The domain wall/QFT correspondence, JHEP 01 (1999) 003 [hep-th/9807137] [INSPIRE].
W. Fischler and S. Kundu, Strongly coupled gauge theories: high and low temperature behavior of non-local observables, JHEP 05 (2013) 098 [arXiv:1212.2643] [INSPIRE].
G. ’t Hooft, The scattering matrix approach for the quantum black hole: an overview, Int. J. Mod. Phys. A 11 (1996) 4623 [gr-qc/9607022] [INSPIRE].
N. Itzhaki, Some remarks on ’t Hooft’s S matrix for black holes, hep-th/9603067 [INSPIRE].
T. Jacobson and R.C. Myers, Black hole entropy and higher curvature interactions, Phys. Rev. Lett. 70 (1993) 3684 [hep-th/9305016] [INSPIRE].
X. Dong, Holographic entanglement entropy for general higher derivative gravity, JHEP 01 (2014) 044 [arXiv:1310.5713] [INSPIRE].
J. Camps, Generalized entropy and higher derivative Gravity, JHEP 03 (2014) 070 [arXiv:1310.6659] [INSPIRE].
A. Buchel, J. Escobedo, R.C. Myers, M.F. Paulos, A. Sinha and M. Smolkin, Holographic GB gravity in arbitrary dimensions, JHEP 03 (2010) 111 [arXiv:0911.4257] [INSPIRE].
M. Taylor, Non-relativistic holography, arXiv:0812.0530 [INSPIRE].
M. Taylor, Lifshitz holography, Class. Quant. Grav. 33 (2016) 033001 [arXiv:1512.03554] [INSPIRE].
M. Alishahiha, A.F. Astaneh and M.R.M. Mozaffar, Thermalization in backgrounds with hyperscaling violating factor, Phys. Rev. D 90 (2014) 046004 [arXiv:1401.2807] [INSPIRE].
P. Fonda, L. Franti, V. Keränen, E. Keski-Vakkuri, L. Thorlacius and E. Tonni, Holographic thermalization with Lifshitz scaling and hyperscaling violation, JHEP 08 (2014) 051 [arXiv:1401.6088] [INSPIRE].
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Sircar, N., Sonnenschein, J. & Tangarife, W. Extending the scope of holographic mutual information and chaotic behavior. J. High Energ. Phys. 2016, 91 (2016). https://doi.org/10.1007/JHEP05(2016)091
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DOI: https://doi.org/10.1007/JHEP05(2016)091