Mutual information and the F-theorem

Abstract

Mutual information is used as a purely geometrical regularization ofentanglement entropy applicable to any QFT. A coefficient in the mutualinformation between concentric circular entangling surfaces gives a preciseuniversal prescription for the monotonous quantity in the c-theorem for d=3.This is in principle computable using any regularization for the entropy, andin particular is a definition suitable for lattice models. We rederive theproof of the c-theorem for d=3 in terms of mutual information, and check ourarguments with holographic entanglement entropy, a free scalar field, and anextensive mutual information model.