Wess-Zumino Consistency Condition for Entanglement Entropy

TL;DR

This paper establishes a Wess-Zumino-like integrability condition governing how entanglement entropy varies with the shape of the entangling surface in field theories coupled to gravity, highlighting localized anomalies.

Contribution

It introduces a novel integrability condition for entanglement entropy variation, linking geometric shape changes to field theory anomalies in a gravitational context.

Findings

Derivation of a Wess-Zumino-like integrability condition

Identification of localized anomalies on the entangling surface

Characterization of finite local terms in entropy variation

Abstract

In this brief note, we consider the variation of the entanglement entropy of a region as the shape of the entangling surface is changed. We show that the variation satisfies a Wess-Zumino like integrability condition in field theories which can be consistently coupled to gravity. In this case the "anomaly" is localized on the entangling surface. The solution of the integrability condition should give all the nontrivial finite local terms which can appear in the variation of the entanglement entropy.