Entanglement Wedge in Flat Holography and Entanglement Negativity

TL;DR

This paper constructs the entanglement wedge in flat holography for 1+1 dimensional Galilean CFTs, proposes a bulk entanglement wedge cross section, and computes entanglement negativity that matches previous results.

Contribution

It introduces a new construction for the entanglement wedge and its cross section in flat space holography, extending holographic entanglement negativity to non-relativistic theories.

Findings

Entanglement negativity matches previous holographic and field theory results.

Constructed entanglement wedge in asymptotically flat geometries.

Generalized entanglement negativity computation to flat space holography.

Abstract

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.