Entanglement and chaos in warped conformal field theories

TL;DR

This work analyzes entanglement and chaotic properties of warped conformal field theories (WCFTs). Using large-c, vacuum-block dominance, it derives the entanglement entropy of excited states and the time evolution of Renyi entropy after a local quench, revealing a memory effect that is nonzero only for charged, spectrally-flowed states and is independent of subsystem size. It also establishes maximal chaos in WCFTs by computing OTOCs in the semiclassical limit, with a Lyapunov exponent saturating the chaos bound, consistent with holographic duals featuring black holes. The results illustrate a rich interplay between the Virasoro and U(1) sectors, spectral flow, and holographic interpretations, and highlight distinctive nonlocal and topological features of WCFT entanglement and chaos.

Abstract

Various aspects of warped conformal field theories (WCFTs) are studied including entanglement entropy on excited states, the Renyi entropy after a local quench, and out-of-time-order four-point functions. Assuming a large central charge and dominance of the vacuum block in the conformal block expansion, (i) we calculate the single-interval entanglement entropy on an excited state, matching previous finite temperature results by changing the ensemble; and (ii) we show that WCFTs are maximally chaotic, a result that is compatible with the existence of black holes in the holographic duals. Finally, we relax the aforementioned assumptions and study the time evolution of the Renyi entropy after a local quench. We find that the change in the Renyi entropy is topological, vanishing at early and late times, and nonvanishing in between only for charged states in spectrally-flowed WCFTs.