Entanglement Entropy Flow and the Ward Identity

Understand

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.