Entanglement entropy: holography and renormalization group

TL;DR

This paper reviews entanglement entropy in quantum field theory and holography, discussing computational methods, divergence structures, and its role in constraining renormalization group flows via quantum inequalities.

Contribution

It provides a comprehensive review of entanglement entropy, including computational techniques, divergence analysis, and its application to the C-theorem in various dimensions.

Findings

Methods for computing entanglement entropy are developed and illustrated.

Ultraviolet divergence structures and universal parts are characterized.

Quantum inequalities of entanglement derive the C-theorem across dimensions.

Abstract

Entanglement entropy plays a variety of roles in quantum field theory, including the connections between quantum states and gravitation through the holographic principle. This article provides a review of entanglement entropy from a mixed viewpoint of field theory and holography. A set of basic methods for the computation is developed and illustrated with simple examples such as free theories and conformal field theories. The structures of the ultraviolet divergences and the universal parts are determined and compared with the holographic descriptions of entanglement entropy. The utility of quantum inequalities of entanglement are discussed and shown to derive the C-theorem that constrains renormalization group flows of quantum field theories in diverse dimensions.