Mutual information and the F-theorem

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.

arXiv comment80 pages, 16 figures

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• Renormalized Entanglement Entropy on Cylinder
• Rényi entropies of the massless Dirac field on the torus
• Quantum correlation in quark-gluon medium