Entanglement Entropy in $T\overline{T}$-Deformed CFT

TL;DR

This paper investigates how $Tar{T}$ deformation affects entanglement entropy in 2D CFTs, revealing nontrivial corrections at finite temperature and confirming holographic duality predictions.

Contribution

It provides the first leading order calculation of entanglement and Rényi entropy corrections due to $Tar{T}$ deformation, including holographic consistency checks.

Findings

Correction to entanglement entropy is nonzero at finite temperature.

Correction vanishes in finite size case.

Holographic entanglement entropy matches the field theory results.

Abstract

In this paper, we study the entanglement entropy of a single interval on a cylinder in two-dimensional $T\overline{T}$-deformed conformal field theory. For such case, the (R\'enyi) entanglement entropy takes a universal form in a CFT. We compute the correction due to the deformation up to the leading order of the deformation parameter in the framework of the conformal perturbation theory. We find that the correction to the entanglement entropy is nonvanishing in the finite temperature case, while it is vanishing in the finite size case. For the deformed holographic large $c$ CFT, which is proposed to be dual to a AdS$_3$ gravity in a finite region, we find the agreement with the holographic entanglement entropy via the Ryu-Takayanagi formula. Moreover, we compute the leading order correction to the R\'enyi entropy, and discuss its holographic picture as well.