Entanglement Entropy and D1-D5 geometries

TL;DR

This paper explores the holographic calculation of entanglement entropy in specific 2D conformal field theories dual to type IIB string theory, focusing on 1/4-BPS microstate geometries and their perturbative analysis for short intervals.

Contribution

It provides a general method for computing entanglement entropy in non-vacuum states of holographic 2D CFTs with asymptotically AdS$_3 imes S^3$ geometries, including analytical perturbative results.

Findings

First non-trivial terms match CFT expectations.

Results align with known vevs of chiral primary operators.

Method applicable to a class of microstate geometries.

Abstract

In Conformal Field Theories with a gravitational AdS dual it is possible to calculate the entanglement entropy of a region $A$ holographically by using the Ryu-Takayanagi formula. In this work we consider systems that are in a pure state that is not the vacuum. We study in particular the 2D Conformal Field Theory dual to type IIB string theory on AdS$_3 \times S^3 \times T^4$ and focus on the $1/4$-BPS states described holographically by the 2-charge microstate geometries. We discuss a general prescription for the calculation of the entanglement entropy in these geometries that are asymptotically AdS$_3 \times S^3$. In particular we study analytically the perturbative expansion for a single, short interval: we show that the first non-trivial terms in this expansion are consistent with the expected CFT structure and with previous results on the vevs of chiral primary operators for the $1/4$-BPS configurations.