Towards entanglement entropy with UV cutoff in conformal nets

TL;DR

This paper introduces a finite entanglement entropy measure with a UV cutoff in conformal nets within algebraic quantum field theory, analyzing its behavior as regions become infinitesimally close.

Contribution

It proposes a new entropic quantity with a UV cutoff in conformal nets and demonstrates its finiteness in the zero-distance limit between regions.

Findings

The entropic measure remains finite as the interval distance approaches zero.

Comparison with existing definitions shows consistency and advantages.

The approach applies to M"obius covariant local nets with nuclearity.

Abstract

We consider the entanglement entropy for a spacetime region and its spacelike complement in the framework of algebraic quantum field theory. For a M\"obius covariant local net satisfying a certain nuclearity property, we consider the von Neumann entropy for type I factors between local algebras and introduce an entropic quantity. Then we implement a cutoff on this quantity with respect to the conformal Hamiltonian and show that it remains finite as the distance of two intervals tends to zero. We compare our definition to others in the literature.