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arXiv:2105.00167 · International Journal of Modern Physics A

Holographic entanglement negativity in flat space generalized minimal massive gravity

Mohammad Reza Setare, M. Koohgard

Published Feb 17, 2022• 8 citations
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Abstract

In this paper, we study the application of holographic entanglement negativity proposal for bipartite states in the 2D Galilean conformal field theory [Formula: see text] dual to bulk asymptotically flat space–times in the context of generalized minimal massive gravity (GMMG) model. [Formula: see text] is considered on the boundary side of the duality and the bulk gravity is described by GMMG that is asymptotically symmetric under the Galilean conformal transformations. In this paper, the replica technique, based on the two-point and the four-point twist correlators, is utilized and the entanglement entropy and the entanglement negativity are obtained in the bipartite configurations of the system in the boundary.

DOI
10.1142/s0217751x22500245

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In this paper, we study the application of holographic entanglement negativity proposal for bipartite states in the 2D Galilean conformal field theory [Formula: see text] dual to bulk asymptotically flat space–times in the context of generalized minimal massive gravity (GMMG) model. [Formula: see text] is considered on the boundary side of the duality and the bulk gravity is described by GMMG that is asymptotically symmetric under the Galilean conformal transformations. In this paper, the replica technique, based on the two-point and the four-point twist correlators, is utilized and the entanglement entropy and the entanglement negativity are obtained in the bipartite configurations of the system in the boundary.
We establish a construction for the entanglement wedge in asymptotically flat bulk geometries for subsystems in dual (1+1)-dimensional Galilean conformal field theories in the context of flat space holography. In this connection we propose a definition for the bulk entanglement wedge cross section for bipartite states of such dual non relativistic conformal field theories. Utilizing our construction for the entanglement wedge cross section we compute the entanglement negativity for such bipartite states through the generalization of an earlier proposal, in the context of the usual AdS/CFT scenario, to flat space holography. The entanglement negativity obtained from our construction exactly reproduces earlier holographic results and match with the corresponding field theory replica technique results in the large central charge limit.
We extend the reflected entropy to the bipartite state in a two dimensional Galilean conformal field theory (GCFT2GCFT_2GCFT2​) 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.
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.
We investigate mixed state entanglement measures of entanglement negativity and reflected entropy for bipartite states in two dimensional conformal field theories with an anomaly through appropriate replica techniques. Furthermore we propose holographic constructions for these measures from the corresponding bulk dual geometries involving topologically massive gravity in AdS3{\mathrm{AdS}}_{3}AdS3​ and find exact agreement with the field theory results. In this connection we extend an earlier holographic proposal for the entanglement negativity to the bulk action with a gravitational Chern-Simons term and compute its contribution to the entanglement wedge cross section dual to the reflected entropy.
We advance a construction for the balanced partial entanglement entropy (BPE) for bipartite mixed states in a class of (1+1)(1+1)(1+1)-dimensional Galilean conformal field theories dual to Einstein gravity and topologically massive gravity in asymptotically flat spacetimes. We compare our results with the entanglement wedge cross section (EWCS) in the dual geometries and find exact agreement. Furthermore, utilizing a geometric picture, we demonstrate the holographic duality between the EWCS and the BPE in the context of flat holography.
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.