State-Dependent Divergences in the Entanglement Entropy

TL;DR

This paper investigates state-dependent divergences in entanglement entropy within quantum field theories, demonstrating their presence in both perturbative and holographic contexts, while showing that certain related quantities remain finite due to divergence cancellations.

Contribution

It classifies all possible state-dependent divergences in perturbatively renormalizable and holographic quantum field theories up to six dimensions.

Findings

Entanglement entropy contains state-dependent divergences.

Relative entropy and black hole entropy remain finite despite divergences.

A comprehensive classification of divergences in relevant quantum field theories.

Abstract

We show the entanglement entropy in certain quantum field theories to contain state-dependent divergences. Both perturbative and holographic examples are exhibited. However, quantities such as the relative entropy and the generalized entropy of black holes remain finite, due to cancellation of divergences. We classify all possible state-dependent divergences that can appear in both perturbatively renormalizeable and holographic covariant $d\le 6$ quantum field theories.