Wess-Zumino Consistency Condition for Entanglement Entropy

Understand

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.