Time evolution of entanglement entropy from a pulse

TL;DR

This paper studies the time evolution of entanglement entropy in a 1+1 dimensional conformal field theory with a holographic dual, focusing on a localized energy pulse, and compares gravity and field theory results.

Contribution

It introduces a finite diffeomorphism that generalizes known transformations to relate AdS space to more general solutions, enabling analysis of entanglement dynamics after a local quench.

Findings

Gravity results match field theory calculations of Rènyi entropy.

Behavior qualitatively agrees with CFT local quench results.

Constructs a generalized diffeomorphism for AdS space.

Abstract

We calculate the time evolution of the entanglement entropy in a 1+1 CFT with a holographic dual when there is a localized left-moving packet of energy density. We find the gravity result agrees with a field theory result derived from the transformation properties of R\'enyi entropy. We are able to reproduce behavior which qualitatively agrees with CFT results of entanglement entropy of a system subjected to a local quench. In doing so we construct a finite diffeomorphism which tales three-dimensional anti-de Sitter space in the Poincar\'e patch to a general solution, generalizing the diffeomorphism that takes the Poincar\'e patch a BTZ black hole. We briefly discuss the calculation of correlation functions in these backgrounds and give results at large operator dimension.