Reflected Entropy in Boundary/Interface Conformal Field Theory

TL;DR

This paper explores the concept of reflected entropy in boundary and interface conformal field theories, establishing holographic dualities with entanglement wedge cross sections and analyzing universal behaviors relevant to the information paradox.

Contribution

It introduces the left-right reflected entropy in BCFT, links it to holographic entanglement wedge cross sections, and extends the analysis to ICFT, providing new insights into boundary correlation functions.

Findings

LRRE in BCFT is dual to entanglement wedge cross section area.

Universal behavior of the Markov gap in certain cases.

Holographic dual of boundary primary correlation functions clarified.

Abstract

Boundary conformal field theory (BCFT) and interface conformal field theory (ICFT) attract attention in the context of the information paradox problem. On this background, we develop the idea of the reflected entropy in BCFT/ICFT. We first introduce the left-right reflected entropy (LRRE) in BCFT and show that its holographic dual is given by the area of the entanglement wedge cross section (EWCS) through AdS/BCFT. We also present how to evaluate the reflected entropy in ICFT. By using this technique, we can show the universal behavior of the Markov gap in some special cases. Furthermore, we clarify what is the holographic dual of boundary primary correlation functions by using this LRRE/EWCS duality.