BCFT in a Black Hole Background: An Analytical Holographic Model

TL;DR

This paper presents an analytical holographic model studying entanglement phase structures of a BCFT in a black hole background, revealing where a Page curve appears and matching gravity and field theory results.

Contribution

It provides the first fully analytical computation of entanglement entropy in a BCFT with a black hole background, elucidating the phase structure and Page curve conditions.

Findings

Analytical match between gravity and field theory entanglement entropy results.

Identification of the phase space where the Page curve exists.

Demonstration of entanglement phase transitions in a curved background.

Abstract

We study the entanglement phase structure of a holographic boundary conformal field theory (BCFT) in a two-dimensional black hole background. The bulk dual is the AdS$_3$ black string geometry with a Karch-Randall brane. We compute the subregion entanglement entropy of various two-sided bipartitions to elucidate the phase space where a Page curve exists in this setup. We do fully analytical computations on both the gravity side and the field theory side and demonstrate that the results precisely match. We discuss the entanglement phase structure describing where a Page curve exists in this geometry in the context of these analytical results. This is a useful model to study entanglement entropy for quantum field theory on a curved background.