Entanglement, $\textrm{T}\bar{\textrm{T}}$ and rotating black holes

TL;DR

This paper explores how $ extrm{T}ar{ extrm{T}}$ deformation affects entanglement properties in a holographic CFT$_2$ with angular momentum, comparing field theory calculations with holographic duals involving rotating black holes.

Contribution

It provides the first detailed comparison of entanglement entropy and reflected entropy corrections in a $ extrm{T}ar{ extrm{T}}$-deformed rotating holographic CFT$_2$ and its dual rotating BTZ black hole.

Findings

Field theory and holographic calculations agree for small deformation parameters.

Leading order corrections to entanglement entropy are computed using conformal perturbation theory.

Holographic entanglement measures match field theory results in the large central charge limit.

Abstract

In this work, we investigate the entanglement structure in a $\textrm{T}\bar{\textrm{T}}$-deformed holographic CFT$_2$ with a conserved angular momentum. We utilize conformal perturbation theory to compute the leading order correction to the entanglement entropy and the reflected entropy due to the $\textrm{T}\bar{\textrm{T}}$ deformation in the limit of large central charge. In the dual bulk perspective described by a rotating BTZ black hole with a finite radial cut-off, we compute the holographic entanglement entropy and the entanglement wedge cross-section and observe perfect agreement with our field theoretic computation for small values of the deformation parameter.