Entanglement Entropy and D1-D5 geometries

TL;DR

This work investigates entanglement entropy (EE) in holographic CFTs for pure states not equal to the vacuum, focusing on the D1-D5 system with type IIB gravity on $AdS_3\times S^3\times T^4$. The authors develop a covariant holographic framework for EE in geometries asymptotic to $AdS_3\times S^3$, derive the geodesic equations for a single interval in 6D microstate geometries, and perform a perturbative short-interval expansion to extract state-specific, non-universal contributions. They map the gravity results to the dual CFT using twist-field OPEs and chiral primaries, fix normalizations via a two-charge geometry, and show that the gravity and CFT results agree for the first non-universal correction at order $l^2$, thereby validating the generalized RT/HRT prescription in this non-vacuum setting. The findings indicate that EE can encode detailed microstate information and motivate future work on higher-BPS configurations, larger intervals, and deeper connections between bulk geometry and boundary entanglement.

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.