Bridging Boundaries: $T\bar{T}$, Double Holography, and Reflected Entropy

TL;DR

This paper explores how $Tar{T}$ deformation affects reflected entropy in 2D BCFTs with holographic duals, analyzing static and dynamic cases, and comparing island and defect extremal surface methods.

Contribution

It provides the first detailed calculation of reflected entropy in $Tar{T}$ deformed holographic BCFTs, including linear order corrections and comparison of different extremal surface prescriptions.

Findings

Leading order correction matches between island and DES prescriptions.

Reflected entropy exhibits modified Page curves due to $Tar{T}$ deformation.

Linear order effects are computed for static and dynamic black hole configurations.

Abstract

We investigate the reflected entropy for bipartite mixed state configurations in a $T\bar{T}$ deformed boundary conformal field theory in $2$ dimensions (BCFT$_2$). The bulk dual is described by asymptotically AdS$_3$ geometries with the cut off surface pushed deeper into the bulk and truncated by an end of the world brane. We obtain the reflected entropy up to a linear order in the radial cut-off for static and time dependent configurations involving an eternal black hole, from the island and defect extremal surface (DES) prescriptions in the context of the deformed AdS/BCFT. We observe agreement of the leading order correction for all cases between the two prescriptions. We also obtain the analogous of the Page curves for the reflected entropy and investigate the modification due to the $T\bar{T}$ deformation.