BCFT and Islands in Two Dimensions

TL;DR

This paper explores the duality between boundary conformal field theories and gravitational systems in two dimensions, focusing on entanglement entropy, boundary conditions, and scalar field effects within the AdS/BCFT framework.

Contribution

It clarifies how BCFT boundary conditions translate into gravitational systems and identifies the dual 2D gravity corresponding to BCFT boundary dynamics.

Findings

Computed entanglement entropy in the dual setup

Reproduced one-point functions using scalar field solutions

Analyzed energy flux conservation in the duality

Abstract

By combining the AdS/BCFT correspondence and the brane world holography, we expect an equivalence relation between a boundary conformal field theory (BCFT) and a gravitational system coupled to a CFT. However, it still remains unclear how the boundary condition of the BCFT is translated in the gravitational system. We examine this duality relation in a two-dimensional setup by looking at the computation of entanglement entropy and energy flux conservation. We also identify the two-dimensional gravity which is dual to the boundary dynamics of a BCFT. Moreover, we show that by considering a gravity solution with scalar fields turned on, we can reproduce one point functions correctly in the AdS/BCFT.