Studies of Boundary Entropy in AdS/BCFT

TL;DR

This paper reviews the AdS/BCFT duality, using entanglement entropy to study boundary effects and impurity entropy, revealing connections between geometric configurations, RG flows, and black hole thermodynamics.

Contribution

It provides new insights into boundary entropy in AdS/BCFT, including finite temperature calculations and geometric interpretations of RG flows.

Findings

Impurity entropy in 2D is state-independent.

Entanglement entropy at finite temperature relates to black hole horizon entropy.

Geometric configurations illustrate RG flows of defect entropies.

Abstract

In this paper we review the AdS/BCFT proposal of T. Takayanagi for holographic description of systems with boundaries, in particular, boundary conformal field theories (BCFTs). Motivated by better understanding of the proposed duality we employ entanglement entropy as a probe of familiar properties of impurities and defects. Using the dual gravity description, we check that in two spacetime dimensions the impurity entropy does not depend on a particular state of the theory, which is a well-known CFT result. In three dimensions different, and not necessarily equivalent, definitions of the defect entropy can be given. We compute the entanglement entropy of a line defect at finite temperature and compare it with earlier calculations of the thermodynamical entropy. The results indicate that the entanglement entropy flows to the definition of the entropy as the Bekenstein-Hawking entropy associated to a portion of the black horizon, which we call impurity "shadow". Geometric configurations, which we discuss, provide examples of RG flows of the defect entropies. We outline the connection between the geometric picture of the RG flows and examples of lattice calculations. We also discuss some new generalizations of the AdS/BCFT geometries.