Entanglement entropy of black holes and AdS/CFT correspondence

TL;DR

This paper extends the Ryu-Takayanagi holographic entanglement entropy proposal to black holes in AdS/CFT, verifying it in specific dimensions and predicting a new universal entropy term related to the obstruction tensor.

Contribution

It generalizes the holographic entanglement entropy proposal to include black holes on the boundary of AdS and predicts a new universal entropy term involving the obstruction tensor.

Findings

Verification of the generalized proposal in d=2 and d=4 dimensions.

Identification of a new entropy term growing as L^2 log L.

Prediction of the obstruction tensor's role in entanglement entropy.

Abstract

A recent proposal by Ryu and Takayanagi for a holographic interpretation of entanglement entropy in conformal field theories dual to supergravity on anti-de Sitter (adS) is generalized to include entanglement entropy of black holes living on the boundary of adS. The generalized proposal is verified in boundary dimensions $d=2$ and $d=4$ for both the UV divergent and UV finite terms. In dimension $d=4$ an expansion of entanglement entropy in terms of size $L$ of the subsystem outside the black hole is considered. A new term in the entropy of dual strongly coupled CFT, which universally grows as $L^2\ln L$ and is proportional to the value of the obstruction tensor at the black hole horizon, is predicted.