Abstract
Motivated by the connection between pole-skipping phenomena of two point functions and four point out-of-time-order correlators, we study the pole-skipping phenomena for rotating BTZ black holes. In particular, we investigate the effect of rotations on the pole-skipping point for various fields with spin s = 1/2, 1, 2/3, extending the previous research for s = 0, 2. We derive an analytic full tower of the pole-skipping points of fermionic (s = 1/2) and vector (s = 1) fields by the exact holographic Green’s functions. For the non-extremal black hole, the leading pole-skipping frequency is ωleading = 2πiTh(s − 1 + νΩ)/(1 − Ω2) where Th is the temperature, Ω the rotation, and ν := (∆+ − ∆−)/2, the difference of conformal dimensions (∆±). These are confirmed by another independent method: the near-horizon analysis. For the extremal black hole, we find that the leading pole-skipping frequency can occur at \( {\omega}_{\textrm{leading}}^{\textrm{extremal}} \) = −2πiTR(s + 1) only when ν = s + 1, where TR is the temperature of the right moving mode. It is non-trivial because it cannot be achieved by simply taking the extreme limit (Th → 0, Ω → 1) of the non-extremal black hole result.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J.M. Maldacena, The Large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [hep-th/9711200] [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
E. Witten, Anti-de Sitter space, thermal phase transition, and confinement in gauge theories, Adv. Theor. Math. Phys. 2 (1998) 505 [hep-th/9803131] [INSPIRE].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [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, R.A. Davison, S. Grozdanov and H. Liu, Many-body chaos and energy dynamics in holography, JHEP 10 (2018) 035 [arXiv:1809.01169] [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].
M. Blake and H. Liu, On systems of maximal quantum chaos, JHEP 05 (2021) 229 [arXiv:2102.11294] [INSPIRE].
H.-S. Jeong, K.-Y. Kim and Y.-W. Sun, Bound of diffusion constants from pole-skipping points: spontaneous symmetry breaking and magnetic field, JHEP 07 (2021) 105 [arXiv:2104.13084] [INSPIRE].
C. Choi, M. Mezei and G. Sárosi, Pole skipping away from maximal chaos, arXiv:2010.08558 [INSPIRE].
F.M. Haehl and M. Rozali, Effective Field Theory for Chaotic CFTs, JHEP 10 (2018) 118 [arXiv:1808.02898] [INSPIRE].
K. Jensen, Scrambling in nearly thermalized states at large central charge, arXiv:1906.05852 [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].
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].
D.M. Ramirez, Chaos and pole skipping in CFT2, JHEP 12 (2021) 006 [arXiv:2009.00500] [INSPIRE].
M. Natsuume and T. Okamura, Nonuniqueness of scattering amplitudes at special points, Phys. Rev. D 104 (2021) 126007 [arXiv:2108.07832] [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].
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, Holographic chaos, pole-skipping, and regularity, PTEP 2020 (2020) 013B07 [arXiv:1905.12014] [INSPIRE].
M. Natsuume and T. Okamura, Pole-skipping with finite-coupling corrections, Phys. Rev. D 100 (2019) 126012 [arXiv:1909.09168] [INSPIRE].
X. Wu, Higher curvature corrections to pole-skipping, JHEP 12 (2019) 140 [arXiv:1909.10223] [INSPIRE].
N. Ceplak, K. Ramdial and D. Vegh, Fermionic pole-skipping in holography, JHEP 07 (2020) 203 [arXiv:1910.02975] [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].
Y. Ahn, V. Jahnke, H.-S. Jeong, K.-Y. Kim, K.-S. Lee and M. Nishida, Pole-skipping of scalar and vector fields in hyperbolic space: conformal blocks and holography, JHEP 09 (2020) 111 [arXiv:2006.00974] [INSPIRE].
N. Abbasi and S. Tahery, Complexified quasinormal modes and the pole-skipping in a holographic system at finite chemical potential, JHEP 10 (2020) 076 [arXiv:2007.10024] [INSPIRE].
Y. Liu and A. Raju, Quantum Chaos in Topologically Massive Gravity, JHEP 12 (2020) 027 [arXiv:2005.08508] [INSPIRE].
Y. Ahn, V. Jahnke, H.-S. Jeong, K.-S. Lee, M. Nishida and K.-Y. Kim, Classifying pole-skipping points, JHEP 03 (2021) 175 [arXiv:2010.16166] [INSPIRE].
M. Natsuume and T. Okamura, Pole-skipping and zero temperature, Phys. Rev. D 103 (2021) 066017 [arXiv:2011.10093] [INSPIRE].
K.-Y. Kim, K.-S. Lee and M. Nishida, Holographic scalar and vector exchange in OTOCs and pole-skipping phenomena, JHEP 04 (2021) 092 [arXiv:2011.13716] [Erratum ibid. 04 (2021) 229] [INSPIRE].
K. Sil, Pole skipping and chaos in anisotropic plasma: a holographic study, JHEP 03 (2021) 232 [arXiv:2012.07710] [INSPIRE].
N. Ceplak and D. Vegh, Pole-skipping and Rarita-Schwinger fields, Phys. Rev. D 103 (2021) 106009 [arXiv:2101.01490] [INSPIRE].
K.-Y. Kim, K.-S. Lee and M. Nishida, Regge conformal blocks from the Rindler-AdS black hole and the pole-skipping phenomena, JHEP 11 (2021) 020 [arXiv:2105.07778] [INSPIRE].
M. Blake and R.A. Davison, Chaos and pole-skipping in rotating black holes, JHEP 01 (2022) 013 [arXiv:2111.11093] [INSPIRE].
K.-Y. Kim, K.-S. Lee and M. Nishida, Construction of bulk solutions for towers of pole-skipping points, Phys. Rev. D 105 (2022) 126011 [arXiv:2112.11662] [INSPIRE].
H.-S. Jeong, K.-Y. Kim and Y.-W. Sun, Quasi-normal modes of dyonic black holes and magneto-hydrodynamics, JHEP 07 (2022) 065 [arXiv:2203.02642] [INSPIRE].
Y.-T. Wang and W.-B. Pan, Pole-skipping of holographic correlators: aspects of gauge symmetry and generalizations, JHEP 01 (2023) 174 [arXiv:2209.04296] [INSPIRE].
D. Wang and Z.-Y. Wang, Pole Skipping in Holographic Theories with Bosonic Fields, Phys. Rev. Lett. 129 (2022) 231603 [arXiv:2208.01047] [INSPIRE].
M.A.G. Amano, M. Blake, C. Cartwright, M. Kaminski and A.P. Thompson, Chaos and pole-skipping in a simply spinning plasma, JHEP 02 (2023) 253 [arXiv:2211.00016] [INSPIRE].
H. Yuan, X.-H. Ge, K.-Y. Kim, C.-W. Ji and Y. Ahn, Pole-skipping points in 2D gravity and SYK model, arXiv:2303.04801 [INSPIRE].
B. Baishya and K. Nayek, Probing Pole Skipping through Scalar-Gauss-Bonnet coupling, arXiv:2301.03984 [INSPIRE].
S. Grozdanov and M. Vrbica, Pole-skipping of gravitational waves in the backgrounds of four-dimensional massive black holes, arXiv:2303.15921 [INSPIRE].
M. Natsuume and T. Okamura, Pole-skipping in a non-black-hole geometry, arXiv:2306.03930 [INSPIRE].
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].
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.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].
B. Craps, S. Khetrapal and C. Rabideau, Chaos in CFT dual to rotating BTZ, JHEP 11 (2021) 105 [arXiv:2107.13874] [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. Banados, C. Teitelboim and J. Zanelli, The Black hole in three-dimensional space-time, Phys. Rev. Lett. 69 (1992) 1849 [hep-th/9204099] [INSPIRE].
M. Banados, M. Henneaux, C. Teitelboim and J. Zanelli, Geometry of the (2 + 1) black hole, Phys. Rev. D 48 (1993) 1506 [gr-qc/9302012] [Erratum ibid. 88 (2013) 069902] [INSPIRE].
N. Iqbal and H. Liu, Real-time response in AdS/CFT with application to spinors, Fortsch. Phys. 57 (2009) 367 [arXiv:0903.2596] [INSPIRE].
S. Das and A. Dasgupta, Black hole emission rates and the AdS/CFT correspondence, JHEP 10 (1999) 025 [hep-th/9907116] [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].
Acknowledgments
We would like to thank Yongjun Ahn, Kyung-Sun Lee, Makoto Natsuume, Mitsuhiro Nishida for valuable discussions and correspondence. This work was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning (NRF-2021R1A2C1006791) and GIST Research Institute(GRI) grant funded by the GIST in 2023. This work was also supported by Creation of the Quantum Information Science R&D Ecosystem (Grant No. 2022M3H3A106307411) through the National Research Foundation of Korea (NRF) funded by the Korean government (Ministry of Science and ICT). H.-S Jeong acknowledges the support of the Spanish MINECO “Centro de Excelencia Severo Ochoa” Programme under grant SEV-2012-0249. This work is supported through the grants CEX2020-001007-S and PID2021-123017NB-I00, funded by MCIN/AEI/10.13039/501100011033 and by ERDF A way of making Europe. C.-W Ji and K.-Y Kim contributed equally to this paper and should be considered co-first authors.
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: 2306.14805
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
Jeong, HS., Ji, CW. & Kim, KY. Pole-skipping in rotating BTZ black holes. J. High Energ. Phys. 2023, 139 (2023). https://doi.org/10.1007/JHEP08(2023)139
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP08(2023)139