Covariant holographic negativity from the entanglement wedge in AdS$_3/$CFT$_2$

TL;DR

This paper introduces a covariant holographic method based on the entanglement wedge cross section to compute entanglement negativity in dynamic AdS$_3$/CFT$_2$ setups, matching previous results up to constants.

Contribution

It proposes a new covariant holographic construction for entanglement negativity using the extremal entanglement wedge cross section, applicable to non-static geometries.

Findings

Accurately reproduces replica technique results in large central charge limit.

Matches previous covariant holographic constructions up to constants.

Applies to rotating BTZ black holes and Vaidya-AdS$_3$ geometries.

Abstract

We propose a covariant holographic construction based on the extremal entanglement wedge cross section, for the entanglement negativity of bipartite states in $CFT_{1+1}$s dual to non static bulk $AdS_3$ geometries. Utilizing our proposal we obtain the holographic entanglement negativity for bipartite mixed states in $CFT_{1+1}$s dual to bulk extremal and non extremal rotating BTZ black holes and the time dependent Vaidya-$AdS_3$ geometries. Our results correctly reproduce the replica technique results modulo certain constants for the corresponding dual $CFT_{1+1}$s in the large central charge limit for the bulk black hole geometries. Furthermore for all the cases our results also match upto such constants with the corresponding results from an earlier alternate covariant holographic construction in the literature. This demonstrates the equivalence modulo constants of the two constructions for the $AdS_3/CFT_2$ scenario.