Entanglement entropy in all dimensions

TL;DR

This paper demonstrates that in higher spacetime dimensions, the entanglement entropy of quantum fields scales proportionally with the boundary area when using Renyi entropy, overcoming divergence issues present in von Neumann entropy.

Contribution

It introduces Renyi entropy as a convergent measure for entanglement in higher dimensions and establishes its proportionality to boundary area, providing new insights into quantum field entanglement.

Findings

Renyi entropy in higher dimensions scales with boundary area.

Divergences in Renyi entropy occur at specific parameters but can be controlled with a mass.

First demonstration of area proportionality of entanglement entropy in all dimensions.

Abstract

It has long been conjectured that the entropy of quantum fields across boundaries scales as the boundary area. This conjecture has not been easy to test in spacetime dimensions greater than four because of divergences in the von Neumann entropy. Here we show that the Renyi entropy provides a convergent alternative, yielding a quantitative measure of entanglement between quantum field theoretic degrees of freedom inside and outside hypersurfaces. For the first time, we show that the entanglement entropy in higher dimensions is proportional to the higher dimensional area. We also show that the Renyi entropy diverges at specific values of the Renyi parameter (q) in each dimension, but this divergence can be tamed by introducing a mass of the quantum field.