Local quenches and quantum chaos from higher spin perturbations

TL;DR

This paper investigates how higher spin charges in 1+1D conformal field theories affect local quenches, entanglement entropy, and chaos, revealing bounds on spin charge, modifications to scrambling time, and conditions for causality.

Contribution

It introduces a Wilson line approach to analyze higher spin effects on entanglement and chaos, establishing bounds and new behaviors in quenched states with higher spin charges.

Findings

Finite entanglement entropy change only if spin charge is bounded by energy.

Scrambling time increases with spin-three charge and diverges at the bound.

Higher spin chemical potential must be bounded to preserve causality and entanglement properties.

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 4\pi/\beta. 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.