Illuminating entanglement shadows of BTZ black holes by a generalized entanglement measure

TL;DR

This paper introduces a generalized entanglement measure in AdS/CFT that accounts for inter-field entanglement and string winding contributions, revealing insights into black hole entanglement shadows and bulk geometry reconstruction.

Contribution

It defines a new entanglement measure incorporating string winding and inter-field entanglement, and demonstrates its ability to probe the entire bulk geometry including entanglement shadows.

Findings

Generalized entanglement measure probes the entire bulk geometry.

Geodesics with non-zero winding relate to the new entanglement measure.

Boundary entanglement structure can reconstruct AdS$_3$ geometries.

Abstract

We define a generalized entanglement measure in the context of the AdS/CFT correspondence. Compared to the ordinary entanglement entropy for a spatial subregion dual to the area of the Ryu-Takayanagi surface, we take into account both entanglement between spatial degrees of freedom as well as between different fields of the boundary theory. Moreover, we resolve the contribution to the entanglement entropy of strings with different winding numbers in the bulk geometry. We then calculate this generalized entanglement measure in a thermal state dual to the BTZ black hole in the setting of the D1/D5 system at and close to the orbifold point. We find that the entanglement entropy defined in this way is dual to the length of a geodesic with non-zero winding number. Such geodesics probe the entire bulk geometry, including the entanglement shadow up to the horizon in the one-sided black hole as well as the wormhole growth in the case of a two-sided black hole for an arbitrarily long time. Therefore, we propose that the entanglement structure of the boundary state is enough to reconstruct asymptotically AdS$_3$ geometries up to extremal surface barriers.