Abstract
We study quantum chaos of rotating BTZ black holes in Topologically Massive gravity (TMG). We discuss the relationship between chaos parameters including Lyapunov exponents and butterfly velocities from shock wave calculations of out-of-time-order correlators (OTOC) and from pole-skipping analysis. We find a partial match between pole-skipping and the OTOC results in the high temperature regime. We also find that the velocity bound puts a chaos constraint on the gravitational Chern-Simons coupling.
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S.H. Shenker and D. Stanford, Black holes and the butterfly effect, JHEP 03 (2014) 067 [arXiv:1306.0622] [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, JHEP 08 (2016) 106 [arXiv:1503.01409] [INSPIRE].
H. Liu and J. Sonner, Quantum many-body physics from a gravitational lens, Nature Rev. Phys. 2 (2020) 615 [arXiv:2004.06159] [INSPIRE].
A. Štikonas, Scrambling time from local perturbations of the rotating BTZ black hole, JHEP 02 (2019) 054 [arXiv:1810.06110] [INSPIRE].
R.R. Poojary, BTZ dynamics and chaos, JHEP 03 (2020) 048 [arXiv:1812.10073] [INSPIRE].
V. Jahnke, K.-Y. Kim and J. Yoon, On the chaos bound in rotating black holes, JHEP 05 (2019) 037 [arXiv:1903.09086] [INSPIRE].
M. Mezei and G. Sárosi, Chaos in the butterfly cone, JHEP 01 (2020) 186 [arXiv:1908.03574] [INSPIRE].
I. Halder, Global symmetry and maximal chaos, arXiv:1908.05281 [INSPIRE].
S. Grozdanov, K. Schalm and V. Scopelliti, Black hole scrambling from hydrodynamics, Phys. Rev. Lett. 120 (2018) 231601 [arXiv:1710.00921] [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].
F.M. Haehl and M. Rozali, Effective field theory for chaotic CFTs, JHEP 10 (2018) 118 [arXiv:1808.02898] [INSPIRE].
F.M. Haehl, W. Reeves and M. Rozali, Reparametrization modes, shadow operators, and quantum chaos in higher-dimensional CFTs, JHEP 11 (2019) 102 [arXiv:1909.05847] [INSPIRE].
M. Blake, R.A. Davison, S. Grozdanov and H. Liu, Many-body chaos and energy dynamics in holography, JHEP 10 (2018) 035 [arXiv:1809.01169] [INSPIRE].
S. Grozdanov, P.K. Kovtun, A.O. Starinets and P. Tadić, The complex life of hydrodynamic modes, JHEP 11 (2019) 097 [arXiv:1904.12862] [INSPIRE].
M. Blake, R.A. Davison and D. Vegh, Horizon constraints on holographic Green’s functions, JHEP 01 (2020) 077 [arXiv:1904.12883] [INSPIRE].
N. Ceplak, K. Ramdial and D. Vegh, Fermionic pole-skipping in holography, JHEP 07 (2020) 203 [arXiv:1910.02975] [INSPIRE].
S. Grozdanov, On the connection between hydrodynamics and quantum chaos in holographic theories with stringy corrections, JHEP 01 (2019) 048 [arXiv:1811.09641] [INSPIRE].
M. Natsuume and T. Okamura, Holographic chaos, pole-skipping, and regularity, PTEP 2020 (2020) 013B07 [arXiv:1905.12014] [INSPIRE].
M. Natsuume and T. Okamura, Nonuniqueness of Green’s functions at special points, JHEP 12 (2019) 139 [arXiv:1905.12015] [INSPIRE].
M. Natsuume and T. Okamura, Pole-skipping with finite-coupling corrections, Phys. Rev. D 100 (2019) 126012 [arXiv:1909.09168] [INSPIRE].
W. Li, S. Lin and J. Mei, Thermal diffusion and quantum chaos in neutral magnetized plasma, Phys. Rev. D 100 (2019) 046012 [arXiv:1905.07684] [INSPIRE].
Y. Ahn, V. Jahnke, H.-S. Jeong and K.-Y. Kim, Scrambling in hyperbolic black holes: shock waves and pole-skipping, JHEP 10 (2019) 257 [arXiv:1907.08030] [INSPIRE].
S. Das, B. Ezhuthachan and A. Kundu, Real time dynamics from low point correlators in 2d BCFT, JHEP 12 (2019) 141 [arXiv:1907.08763] [INSPIRE].
X. Wu, Higher curvature corrections to pole-skipping, JHEP 12 (2019) 140 [arXiv:1909.10223] [INSPIRE].
N. Abbasi and J. Tabatabaei, Quantum chaos, pole-skipping and hydrodynamics in a holographic system with chiral anomaly, JHEP 03 (2020) 050 [arXiv:1910.13696] [INSPIRE].
S. Deser, R. Jackiw and S. Templeton, Topologically massive gauge theories, Annals Phys. 140 (1982) 372 [Erratum ibid. 185 (1988) 406] [INSPIRE].
S. Deser, R. Jackiw and S. Templeton, Three-dimensional massive gauge theories, Phys. Rev. Lett. 48 (1982) 975 [INSPIRE].
M.-I. Park, BTZ black hole with gravitational Chern-Simons: thermodynamics and statistical entropy, Phys. Rev. D 77 (2008) 026011 [hep-th/0608165] [INSPIRE].
W. Li, W. Song and A. Strominger, Chiral gravity in three dimensions, JHEP 04 (2008) 082 [arXiv:0801.4566] [INSPIRE].
M. Bañados, C. Teitelboim and J. Zanelli, The black hole in three-dimensional space-time, Phys. Rev. Lett. 69 (1992) 1849 [hep-th/9204099] [INSPIRE].
M. Bañados, M. Henneaux, C. Teitelboim and J. Zanelli, Geometry of the (2 + 1) black hole, Phys. Rev. D 48 (1993) 1506 [Erratum ibid. 88 (2013) 069902] [gr-qc/9302012] [INSPIRE].
S. Carlip, The (2 + 1)-dimensional black hole, Class. Quant. Grav. 12 (1995) 2853 [gr-qc/9506079] [INSPIRE].
D. Birmingham, I. Sachs and S.N. Solodukhin, Conformal field theory interpretation of black hole quasinormal modes, Phys. Rev. Lett. 88 (2002) 151301 [hep-th/0112055] [INSPIRE].
D.T. Son and A.O. Starinets, Minkowski space correlators in AdS/CFT correspondence: Recipe and applications, JHEP 09 (2002) 042 [hep-th/0205051] [INSPIRE].
A. Castro, S. Detournay, N. Iqbal and E. Perlmutter, Holographic entanglement entropy and gravitational anomalies, JHEP 07 (2014) 114 [arXiv:1405.2792] [INSPIRE].
P. Kraus and F. Larsen, Holographic gravitational anomalies, JHEP 01 (2006) 022 [hep-th/0508218] [INSPIRE].
K. Skenderis, M. Taylor and B.C. van Rees, Topologically massive gravity and the AdS/CFT correspondence, JHEP 09 (2009) 045 [arXiv:0906.4926] [INSPIRE].
V. Balasubramanian and P. Kraus, A stress tensor for Anti-de Sitter gravity, Commun. Math. Phys. 208 (1999) 413 [hep-th/9902121] [INSPIRE].
S. de Haro, S.N. Solodukhin and K. Skenderis, Holographic reconstruction of space-time and renormalization in the AdS/CFT correspondence, Commun. Math. Phys. 217 (2001) 595 [hep-th/0002230] [INSPIRE].
P. Sabella-Garnier, K. Schalm, T. Vakhtel and J. Zaanen, Thermalization/relaxation in integrable and free field theories: an operator thermalization hypothesis, arXiv:1906.02597 [INSPIRE].
S.S. Gubser, Absorption of photons and fermions by black holes in four-dimensions, Phys. Rev. D 56 (1997) 7854 [hep-th/9706100] [INSPIRE].
I. Bredberg, T. Hartman, W. Song and A. Strominger, Black hole superradiance from Kerr/CFT, JHEP 04 (2010) 019 [arXiv:0907.3477] [INSPIRE].
M. Alishahiha, A. Davody, A. Naseh and S.F. Taghavi, On butterfly effect in higher derivative gravities, JHEP 11 (2016) 032 [arXiv:1610.02890] [INSPIRE].
D. Grumiller and N. Johansson, Instability in cosmological topologically massive gravity at the chiral point, JHEP 07 (2008) 134 [arXiv:0805.2610] [INSPIRE].
K. Sfetsos, On gravitational shock waves in curved space-times, Nucl. Phys. B 436 (1995) 721 [hep-th/9408169] [INSPIRE].
D.A. Roberts and D. Stanford, Two-dimensional conformal field theory and the butterfly effect, Phys. Rev. Lett. 115 (2015) 131603 [arXiv:1412.5123] [INSPIRE].
S. Xu, X. Li, Y.-T. Hsu, B. Swingle and S. Das Sarma, Butterfly effect in interacting Aubry-Andre model: thermalization, slow scrambling, and many-body localization, Phys. Rev. Res. 1 (2019) 032039 [arXiv:1902.07199].
I. Sachs and S.N. Solodukhin, Quasi-normal modes in topologically massive gravity, JHEP 08 (2008) 003 [arXiv:0806.1788] [INSPIRE].
D.M. Ramirez, Chaos and pole skipping in CFT2, arXiv:2009.00500 [INSPIRE].
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Liu, Y., Raju, A. Quantum chaos in topologically massive gravity. J. High Energ. Phys. 2020, 27 (2020). https://doi.org/10.1007/JHEP12(2020)027
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DOI: https://doi.org/10.1007/JHEP12(2020)027