Aspects of Holographic Entanglement Entropy

TL;DR

This paper explores the holographic interpretation of entanglement entropy within the AdS/CFT framework, providing new derivations, extending to higher dimensions, and comparing results with conformal field theory calculations.

Contribution

It offers a more direct derivation of the holographic entanglement entropy relation and extends the analysis to higher dimensions and massive theories.

Findings

Derivation of entanglement entropy as minimal surface area in AdS_3/CFT_2

Analysis of entanglement entropy and central charges in 4D CFTs

Estimation of entanglement entropy in massive theories across dimensions

Abstract

This is an extended version of our short report hep-th/0603001, where a holographic interpretation of entanglement entropy in conformal field theories is proposed from AdS/CFT correspondence. In addition to a concise review of relevant recent progresses of entanglement entropy and details omitted in the earlier letter, this paper includes the following several new results : We give a more direct derivation of our claim which relates the entanglement entropy with the minimal area surfaces in the AdS_3/CFT_2 case as well as some further discussions on higher dimensional cases. Also the relation between the entanglement entropy and central charges in 4D conformal field theories is examined. We check that the logarithmic part of the 4D entanglement entropy computed in the CFT side agrees with the AdS_5 result at least under a specific condition. Finally we estimate the entanglement entropy of massive theories in generic dimensions by making use of our proposal.