The reflected entropy in the GMMG/GCFT flat holography

TL;DR

This paper extends the concept of reflected entropy to bipartite states in 2D Galilean conformal field theories dual to flat spacetimes, revealing a relation to entanglement wedge cross sections in flat holography.

Contribution

It introduces a method to compute reflected entropy in GCFT_2 and establishes its proportionality to the entanglement wedge cross section in flat holography.

Findings

Reflected entropy is twice the minimal entanglement wedge cross section in certain cases.

Provides a new link between reflected entropy and geometric quantities in flat holography.

Extends the holographic entanglement entropy framework to flat spacetime scenarios.

Abstract

We extend the reflected entropy to the bipartite state in a two dimensional Galilean conformal field theory ($GCFT_2$) which is dual to the asymptotically flat spacetime described by the generalized minimal massive gravity (GMMG). To this end we consider the Renyi entanglement entropy formula that can be related to the reflected entropy by some manipulations of the replica technique. In a limited case, we find the reflected entropy is twice the minimal entanglement wedge cross section (EWCS) and this is an evidence on the relation between the reflected entropy and the EWCS in the flat holography scenario.