Entanglement Entropy Flow and the Ward Identity

TL;DR

This paper establishes a formal connection between the flow of entanglement entropy, metric variations, and the Ward identity, providing a new way to compute entanglement entropy in quantum field theories.

Contribution

It derives differential equations describing entanglement entropy flow and links its variation under Weyl transformations to the trace Ward identity, offering a novel computational approach.

Findings

Entanglement entropy variation relates to the trace Ward identity.

Expressed entanglement entropy for free fields as a two-point function.

Derived differential equations for entanglement entropy flow.

Abstract

We derive differential equations for the flow of entanglement entropy as a function of the metric and the couplings of the theory. The variation of the universal part of entanglement entropy under a local Weyl transformation is related to the variation under a local change in the couplings. We show that this relation is in fact equivalent to the trace Ward identity. As a concrete application of our formalism, we express the entanglement entropy for massive free fields as a two-point function of the energy-momentum tensor.