Holographic entanglement entropy in $T\overline{T}$-deformed AdS$_3$

TL;DR

This paper investigates the holographic entanglement entropy in $Tar{T}$-deformed AdS$_3$ gravity, providing a consistent calculation using multiple methods and exploring the effects of deformation on entanglement properties and phase transitions.

Contribution

It presents a novel calculation of holographic entanglement entropy in $Tar{T}$-deformed AdS$_3$ using Chern-Simons and RT surface methods, aligning with perturbative results.

Findings

Holographic entanglement entropy matches perturbative calculations.

Deformed entropy at large deformation resembles zero-temperature CFT entropy.

$Tar{T}$ deformation influences phase transition behavior in entanglement entropy.

Abstract

In this work, we study the holographic entanglement entropy in AdS$_3$ gravity with the certain mixed boundary condition, which turns out to correspond to $T\bar{T}$-deformed 2D CFTs. By employing the Chern-Simons formalism and Wilson line technique, the holographic entanglement entropy in $T\bar{T}$-deformed BTZ black hole is obtained. We also get the same formula by calculating the RT surface. The holographic entanglement entropy agrees with the perturbation result derived from both $T\bar{T}$-deformed CFTs and cutoff AdS$_3$. Moreover, our result shows that the deformed entanglement entropy for large deformation parameter behaves like the entanglement entropy of CFT at zero temperature. We also consider the entanglement entropy of two intervals and study the effect of $T\bar{T}$ deformation on phase transition.