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arXiv:2201.11741

The reflected entropy in the GMMG/GCFT flat holography

Mohammad Reza Setare, M. Koohgard

Published Jan 1, 2022• 0 citations
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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.

DOI
10.48550/arxiv.2201.11741

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Abstract The odd entanglement entropy (OEE) for bipartite states in a class of (1+1)(1+1)(1+1) ( 1 + 1 ) -dimensional Galilean conformal field theories ( GCFT1+1GCFT_{1+1}GCFT1+1​ G C F T 1 + 1 ) is obtained through an appropriate replica technique. In this context our results are compared with the entanglement wedge cross section (EWCS) for (2+1)(2+1)(2+1) ( 2 + 1 ) -dimensional asymptotically flat geometries dual to the GCFT1+1GCFT_{1+1}GCFT1+1​ G C F T 1 + 1 in the framework of flat holography. We find that our results are consistent with the duality of the difference between the odd entanglement entropy and the entanglement entropy of bipartite states, with the bulk EWCS for flat holographic scenarios.
We focus on a proper candidate for the entanglement wedge in asymptotically flat bulk geometries that are described by the generalized minimal massive gravity (GMMG) in the context of the flat holography. To this end, we describe the boundary by two dimensional Galilean conformal field theory (GCFT) at the bipartite mixed state of the two disjoint intervals. We derive an analytic expression for the minimal entanglement wedge cross section (EWCS) in the GMMG/GCFT framework. Our result provides an independent derivation that precisely matches previous computations of holographic entanglement negativity, thereby offering a powerful consistency check and validating both approaches within the GMMG/GCFT framework.
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