Abstract
We study local quenches in 1+1 dimensional conformal field theories at large-c by operators carrying higher spin charge. Viewing such states as solutions in Chern-Simons theory, representing infalling massive particles with spin-three charge in the BTZ back-ground, we use the Wilson line prescription to compute the single-interval entanglement entropy (EE) and scrambling time following the quench. We find that the change in EE is finite (and real) only if the spin-three charge q is bounded by the energy of the perturbation E, as |q|/c < E 2 /c 2. We show that the Wilson line/EE correlator deep in the quenched regime and its expansion for small quench widths overlaps with the Regge limit for chaos of the out-of-time-ordered correlator. We further find that the scrambling time for the two-sided mutual information between two intervals in the thermofield double state increases with increasing spin-three charge, diverging when the bound is saturated. For larger values of the charge, the scrambling time is shorter than for pure gravity and controlled by the spin-three Lyapunov exponent 4π/β. In a CFT with higher spin chemical potential, dual to a higher spin black hole, we find that the chemical potential must be bounded to ensure that the mutual information is a concave function of time and entanglement speed is less than the speed of light. In this case, a quench with zero higher spin charge yields the same Lyapunov exponent as pure Einstein gravity.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S.H. Shenker and D. Stanford, Black holes and the butterfly effect, JHEP 03 (2014) 067 [arXiv:1306.0622] [INSPIRE].
J. Maldacena, S.H. Shenker and D. Stanford, A bound on chaos, JHEP 08 (2016) 106 [arXiv:1503.01409] [INSPIRE].
S.H. Shenker and D. Stanford, Multiple shocks, JHEP 12 (2014) 046 [arXiv:1312.3296] [INSPIRE].
S.H. Shenker and D. Stanford, Stringy effects in scrambling, JHEP 05 (2015) 132 [arXiv:1412.6087] [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].
A. Kitaev, A simple model of quantum holography, KITP program on Entanglement (2015).
E. Perlmutter, Bounding the space of holographic CFTs with chaos, JHEP 10 (2016) 069 [arXiv:1602.08272] [INSPIRE].
T. Hartman, Entanglement Entropy at Large Central Charge, arXiv:1303.6955 [INSPIRE].
C.T. Asplund, A. Bernamonti, F. Galli and T. Hartman, Holographic entanglement entropy from 2d CFT: heavy states and local quenches, JHEP 02 (2015) 171 [arXiv:1410.1392] [INSPIRE].
J. de Boer, A. Castro, E. Hijano, J.I. Jottar and P. Kraus, Higher spin entanglement and \( {\mathcal{W}}_{\mathrm{N}} \) conformal blocks, JHEP 07 (2015) 168 [arXiv:1412.7520] [INSPIRE].
M. Besken, A. Hegde, E. Hijano and P. Kraus, Holographic conformal blocks from interacting Wilson lines, JHEP 08 (2016) 099 [arXiv:1603.07317] [INSPIRE].
P. Calabrese and J. Cardy, Entanglement and correlation functions following a local quench: a conformal field theory approach, J. Stat. Mech. 0710 (2007) P10004 [arXiv:0708.3750] [INSPIRE].
M. Nozaki, T. Numasawa and T. Takayanagi, Holographic local quenches and entanglement density, JHEP 05 (2013) 080 [arXiv:1302.5703] [INSPIRE].
M. Nozaki, T. Numasawa and T. Takayanagi, Quantum Entanglement of Local Operators in Conformal Field Theories, Phys. Rev. Lett. 112 (2014) 111602 [arXiv:1401.0539] [INSPIRE].
S. He, T. Numasawa, T. Takayanagi and K. Watanabe, Quantum dimension as entanglement entropy in two dimensional conformal field theories, Phys. Rev. D 90 (2014) 041701 [arXiv:1403.0702] [INSPIRE].
P. Caputa, M. Nozaki and T. Takayanagi, Entanglement of local operators in large-N conformal field theories, PTEP 2014 (2014) 093B06 [arXiv:1405.5946] [INSPIRE].
J.R. David, S. Khetrapal and S.P. Kumar, Universal corrections to entanglement entropy of local quantum quenches, JHEP 08 (2016) 127 [arXiv:1605.05987] [INSPIRE].
P. Caputa, J. Simón, A. Štikonas and T. Takayanagi, Quantum entanglement of localized excited states at finite temperature, JHEP 01 (2015) 102 [arXiv:1410.2287] [INSPIRE].
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].
J. de Boer and J.I. Jottar, Entanglement Entropy and Higher Spin Holography in AdS 3, JHEP 04 (2014) 089 [arXiv:1306.4347] [INSPIRE].
M. Ammon, A. Castro and N. Iqbal, Wilson lines and entanglement entropy in higher spin gravity, JHEP 10 (2013) 110 [arXiv:1306.4338] [INSPIRE].
S. Datta, J.R. David, M. Ferlaino and S.P. Kumar, Higher spin entanglement entropy from CFT, JHEP 06 (2014) 096 [arXiv:1402.0007] [INSPIRE].
S. Datta, J.R. David, M. Ferlaino and S.P. Kumar, Universal correction to higher spin entanglement entropy, Phys. Rev. D 90 (2014) 041903 [arXiv:1405.0015] [INSPIRE].
M. Gutperle and P. Kraus, Higher spin black holes, JHEP 05 (2011) 022 [arXiv:1103.4304] [INSPIRE].
M. Ammon, M. Gutperle, P. Kraus and E. Perlmutter, Black holes in three dimensional higher spin gravity: a review, J. Phys. A 46 (2013) 214001 [arXiv:1208.5182] [INSPIRE].
P. Calabrese and J.L. Cardy, Evolution of entanglement entropy in one-dimensional systems, J. Stat. Mech. 0504 (2005) P04010 [cond-mat/0503393] [INSPIRE].
T. Hartman and J. Maldacena, Time evolution of entanglement entropy from black hole interiors, JHEP 05 (2013) 014 [arXiv:1303.1080] [INSPIRE].
A. Castro, N. Iqbal and E. Llabrés, Eternal higher spin black holes: a thermofield interpretation, JHEP 08 (2016) 022 [arXiv:1602.09057] [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 and J.I. Jottar, Thermodynamics of higher spin black holes in AdS 3, JHEP 01 (2014) 023 [arXiv:1302.0816] [INSPIRE].
M. Bañados, Three-dimensional quantum geometry and black holes, AIP Conf. Proc. 484 (1999) 147 [hep-th/9901148] [INSPIRE].
I. Ya. Aref’eva, M.A. Khramtsov and M.D. Tikhanovskaya, Thermalization after holographic bilocal quench, JHEP 09 (2017) 115 [arXiv:1706.07390] [INSPIRE].
J.R. David, M. Ferlaino and S.P. Kumar, Thermodynamics of higher spin black holes in 3D, JHEP 11 (2012) 135 [arXiv:1210.0284] [INSPIRE].
S. Datta, Relative entropy in higher spin holography, Phys. Rev. D 90 (2014) 126010 [arXiv:1406.0520] [INSPIRE].
J. Long, Higher spin entanglement entropy, JHEP 12 (2014) 055 [arXiv:1408.1298] [INSPIRE].
J. Erdmenger, D. Fernandez, M. Flory, E. Megias, A.-K. Straub and P. Witkowski, Time evolution of entanglement for holographic steady state formation, JHEP 10 (2017) 034 [arXiv:1705.04696] [INSPIRE].
A. Allais and E. Tonni, Holographic evolution of the mutual information, JHEP 01 (2012) 102 [arXiv:1110.1607] [INSPIRE].
B. Chen and J.-q. Wu, Higher spin entanglement entropy at finite temperature with chemical potential, JHEP 07 (2016) 049 [arXiv:1604.03644] [INSPIRE].
N. Afkhami-Jeddi, K. Colville, T. Hartman, A. Maloney and E. Perlmutter, Constraints on Higher Spin CFT 2, arXiv:1707.07717 [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: 1707.07166
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
David, J.R., Khetrapal, S. & Kumar, S.P. Local quenches and quantum chaos from higher spin perturbations. J. High Energ. Phys. 2017, 156 (2017). https://doi.org/10.1007/JHEP10(2017)156
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2017)156