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 < E2/c2. 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.
Highlights
The incorporation of ideas from quantum chaos is an exciting development in the study of real time dynamics of quantum field theories (QFTs) and its implications for gravitational systems which are holographically dual to them [1,2,3,4,5,6,7]
In a conformal field theories (CFTs) 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
We focus our attention on two questions which can both be answered with currently known CFT and bulk results at finite spin three chemical potential
Summary
The incorporation of ideas from quantum chaos is an exciting development in the study of real time dynamics of quantum field theories (QFTs) and its implications for gravitational systems which are holographically dual to them [1,2,3,4,5,6,7]. We compute such Wilson lines in a static, spin-three charged, conical deficit state, characterised by a flat Chern-Simons connection, and act on the result by the same boundary conformal transformation which maps the uncharged deficits to infalling massive particles in the BTZ background This is interpreted as a finite width local quench by an operator carrying spin-three charge, with the CFT originally in the zero charge thermal ensemble.. The four-point correlator of the type (2.1) which yields the single interval entanglement entropy in the locally quenched quantum state is computed by a Wilson line in the asymptotically AdS3 shockwave background. 2π β which controls the late time, exponential departure of the OTO correlator from its constant value.4 Note that this does not dictate the behaviour of the single interval entanglement entropy following the local quench.
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