Holographic entanglement negativity conjecture for adjacent intervals in $AdS_3/CFT_2$

TL;DR

This paper proposes a holographic conjecture for entanglement negativity of adjacent intervals in 2D CFTs using $AdS_3/CFT_2$, reproducing known CFT results and extending to finite temperature cases.

Contribution

It introduces a new holographic entanglement negativity conjecture based on bulk geometry, specifically involving geodesics and mutual information, for adjacent intervals in 2D CFTs.

Findings

Conjecture reproduces CFT results at large central charge.

Applies to zero and finite temperature cases.

Provides a geometric interpretation of entanglement negativity.

Abstract

We propose a holographic entanglement negativity conjecture involving the bulk geometry, for mixed states of adjacent intervals in $(1+1)$-dimensional dual conformal field theories through the $AdS/CFT$ correspondence. The holographic entanglement negativity is obtained from a specific algebraic sum of the geodesics anchored on respective intervals on the boundary which reduces to the holographic mutual information between them. Utilizing our conjecture we obtain the entanglement negativity of adjacent intervals in zero and finite temperature ($1+1$)-dimensional holographic conformal field theories dual to the bulk $AdS_3$ vacuum and the Euclidean BTZ black hole respectively. Our holographic conjecture exactly reproduces the conformal field theory results obtained through the replica technique, in the large central charge limit. We briefly elucidate the corresponding issue for the $AdS_{d+1}/CFT_d$ scenario.