Holographic boundary conformal field theory with $T\bar T$ deformation

TL;DR

This paper proposes a holographic dual for boundary conformal field theories with $Tar T$ deformation, analyzing boundary effects, energy spectra, and entanglement entropy to establish a consistent duality framework.

Contribution

It introduces a novel holographic dual for $Tar T$ BCFTs, distinguishing boundary-deformed and undeformed cases, and computes key physical quantities to support the duality.

Findings

Boundary entropy quantifies boundary deformation effects.

Energy spectrum matches between field theory and gravity calculations.

Entanglement and Rénnyi entropies agree across dual descriptions.

Abstract

We propose a holographic dual of boundary conformal field theory (BCFT) with $T\bar T$ deformation, i.e. of $T\bar T$ BCFT. Our holographic proposal distinguishes two types of $T\bar T$ BCFTs, depending on whether the $T\bar T$ deformation deforms the boundary. For the boundary-deformed case, we find that boundary entropy serves as an effective measure to quantify the impact of boundary deformation. In this scenario, we calculate the energy spectrum for the $T\bar T$ BCFT within a finite interval to support the proposed dual. For the boundary-undeformed case, we calculate the entanglement entropy and R\'enyi entropy from both the field theory side and the gravity side, and find that they match.