A c-theorem for the entanglement entropy

TL;DR

This paper establishes a c-theorem for entanglement entropy in 1+1 dimensions using Lorentz symmetry and strong subadditivity, compares it with Zamolodchikov's c-function, and discusses challenges in extending it to higher dimensions.

Contribution

It provides a simple derivation of the entropic c-theorem in 1+1 dimensions and analyzes its relation to existing c-functions, highlighting difficulties in higher dimensions.

Findings

Derived a c-theorem for entanglement entropy in 1+1D

Compared entropic c-functions with Zamolodchikov's functions for free fields

Discussed obstacles to generalizing the entropic c-theorem to higher dimensions

Abstract

The combination of the Lorentz symmetry and the strong subadditive property of the entropy leads to a c-theorem for the entanglement entropy in 1+1 dimensions. We present a simple derivation of this theorem and compare the associated c-functions with the Zamolodchikov's ones for the case of free fields. We discuss the various difficulties which obstacle the naive generalizations of the entropic c-theorem to higher dimensions.