Covariant Holographic Entanglement Negativity for Adjacent Subsystems in $\mathrm{AdS_{3}/CFT_2}$

TL;DR

This paper introduces a covariant holographic method to compute entanglement negativity for time-dependent mixed states of adjacent intervals in 1+1 dimensional CFTs, matching known results for rotating BTZ black holes and Vaidya-AdS configurations.

Contribution

It proposes a new covariant holographic construction for entanglement negativity applicable to dynamic AdS_3/CFT_2 scenarios, extending previous static approaches.

Findings

Reproduces replica technique results for rotating BTZ black holes.

Derives time-dependent negativity for Vaidya-AdS_3 configurations.

Validates the conjecture in large central charge limit.

Abstract

We propose a covariant holographic entanglement negativity constructionfor time-dependent mixed states of adjacent intervals in $(1+1)$-dimensional conformal field theories dual to non-static bulk $\mathrm{AdS_3}$ configurations. Our construction applied to $(1+1)$-dimensional conformal field theories with a conserved charge dual to non-extremal and extremal rotating BTZ black holes exactly reproduces the corresponding replica technique results, in the large central charge limit. We also utilize our conjecture to obtain the time-dependent holographic entanglement negativity for the mixed state in question for the $(1+1)$- dimensional CFT dual to a bulk Vaidya-$\mathrm{AdS_3}$ configuration.