Entanglement negativity in $\text{T}\bar{\text{T}}$-deformed CFT$_2$s

TL;DR

This paper develops a perturbative method to compute entanglement negativity in T$ar{ ext{T}}$-deformed CFT$_2$s and compares field theory results with holographic dual calculations, confirming consistency at small deformations.

Contribution

It introduces a first-order perturbative approach for entanglement negativity in T$ar{ ext{T}}$-deformed CFT$_2$s and extends holographic dual computations to these deformed theories.

Findings

Perturbative expression for negativity up to first order in deformation.

Agreement between field theory and holographic results at small deformation.

Explicit calculations for various bipartite states at finite temperature.

Abstract

We apply a suitable replica technique to develop a perturbative expression for the entanglement negativity of bipartite mixed states in T$\overline{\text{T}}$-deformed CFT$_2$s up to the first order in the deformation parameter. Utilizing our perturbative construction we compute the entanglement negativity for various bipartite mixed states involving two disjoint intervals, two adjacent intervals, and a single interval in a T$\overline{\text{T}}$-deformed CFT$_2$ at a finite temperature, in the large central charge limit. Subsequently, we advance appropriate holographic constructions to compute the entanglement negativity for such bipartite states in T$\overline{\text{T}}$-deformed thermal CFT$_2$s dual to BTZ black holes in a finite cut-off bulk geometry and find agreement with the corresponding field theoretic results in the limit of small deformation parameter.