Entanglement Entropy, Trace Anomalies and Holography

TL;DR

This paper investigates the holographic calculation of entanglement entropy in four-dimensional conformal field theories, comparing two methods and analyzing discrepancies for complex geometries.

Contribution

It introduces a generalized replica trick for evaluating anomalous entanglement entropy terms and compares holographic methods without solving equations of motion.

Findings

Discrepancies found between two holographic calculation methods for generic geometries.

Analysis of reasons behind the disagreement between methods.

Insights into the holographic representation of entanglement entropy and trace anomalies.

Abstract

The holographic representation of the entanglement entropy of four dimensional conformal field theories is studied. By generalizing the replica trick the anomalous terms in the entanglement entropy are evaluated. The same terms in the holographic representation are calculated by a method which does not require the solution of the equations of motion or a cut off. The two calculations disagree for rather generic geometries. The reasons for the disagreement are analyzed.