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.
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© 2014 American Physical Society.