Relative R\'enyi Entropy Under Local Quenches in 2D CFTs

TL;DR

This paper investigates the behavior of relative Rènyi entropy under local quenches in 2D CFTs, revealing monotonic evolution in RCFTs, connections to trace distance, and insights into bulk geometry in holographic theories.

Contribution

It provides a detailed analysis of RRE dynamics in RCFTs and holographic CFTs, linking quantum information measures to bulk geometry and subsystem distinguishability.

Findings

RRE evolves monotonically in RCFTs

Symmetry observed in RRE relates to trace squared distance

Analytic continuation of RRE offers insights into entanglement wedge

Abstract

We study the relative R\'enyi entropy (RRE) under local quenches in two-dimensional conformal field theories (CFTs), focusing on rational CFTs (RCFTs) and holographic CFTs. In RCFTs, the RRE evolves as a monotonic function over time, depending on finite-dimensional matrices. It is sometimes symmetric, prompting an exploration of its relation to the trace squared distance. We also observe that relative entropy can fail to distinguish between operators, as it only captures information entering/exiting the subsystem. In holographic CFTs, an analytic continuation of the RRE reveals insights into the entanglement wedge, offering a new perspective on bulk geometry in AdS/CFT. Our results deepen the understanding of quantum information measures in RCFTs and holographic CFTs, highlighting connections to distinguishability and bulk reconstruction.