paper

Local quenches and quantum chaos from higher spin perturbations

arXiv:1707.07166 · doi:10.1007/JHEP10(2017)156

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 background, 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.

arXiv commentReplaced with version to appear in JHEP. Discussion included to clarify compatibility of the bound deduced in this paper with that of arXiv: 1707.07717

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