Mutual information and the F-theorem

TL;DR

This paper introduces a universal, geometrical approach using mutual information to define a monotonous quantity in the c-theorem for three-dimensional quantum field theories, applicable across various models and regularizations.

Contribution

It provides a new universal prescription for the c-theorem in d=3 using mutual information, with proofs and checks across holographic, free scalar, and mutual information models.

Findings

Mutual information defines a universal c-theorem quantity in d=3.

The approach is compatible with lattice regularizations.

Validation through holographic and free scalar field models.

Abstract

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