Entanglement Negativity in Flat Holography

TL;DR

This paper develops a holographic method to compute entanglement negativity in 1+1 dimensional Galilean conformal field theories, using algebraic sums of extremal bulk curves, matching replica technique results in the large central charge limit.

Contribution

It introduces a new holographic construction for entanglement negativity in flat holography, extending previous methods to Galilean conformal field theories and asymptotically flat geometries.

Findings

Exact reproduction of replica technique results in large central charge limit

Construction validated through semi classical geometric monodromy analysis

Applicable to bipartite states in Galilean conformal field theories

Abstract

We advance holographic constructions for the entanglement negativity of bipartite states in a class of $(1+1)-$dimensional Galilean conformal field theories dual to asymptotically flat three dimensional bulk geometries described by Einstein Gravity and Topologically Massive Gravity. The construction involves specific algebraic sums of the lengths of bulk extremal curves homologous to certain combinations of the intervals appropriate to such bipartite states. Our analysis exactly reproduces the corresponding replica technique results in the large central charge limit. We substantiate our construction through a semi classical analysis involving the geometric monodromy technique for the case of two disjoint intervals in such Galilean conformal field theories dual to bulk Einstein Gravity.