Momentum-space entanglement in scalar field theory on fuzzy spheres

TL;DR

This paper explores how noncommutative geometry affects quantum correlations by calculating momentum-space entanglement entropy in scalar field theory on fuzzy spheres, revealing unique behaviors due to nonlocality and matrix regularization.

Contribution

It provides the first explicit evaluation of momentum-space entanglement entropy on fuzzy spheres, highlighting differences from continuous spheres and analyzing the impact of non-planar contributions.

Findings

Entanglement entropy behaves differently on fuzzy spheres compared to continuous spheres.

Mutual information between low and high momentum modes shows distinct scaling with cutoff effects.

Differences are attributed to non-planar contributions and matrix regularization characteristics.

Abstract

Quantum field theory defined on a noncommutative space is a useful toy model of quantum gravity and is known to have several intriguing properties, such as nonlocality and UV/IR mixing. They suggest novel types of correlation among the degrees of freedom of different energy scales. In this paper, we investigate such correlations by the use of entanglement entropy in the momentum space. We explicitly evaluate the entanglement entropy of scalar field theory on a fuzzy sphere and find that it exhibits different behaviors from that on the usual continuous sphere. We argue that these differences would originate in different characteristics; non-planar contributions and matrix regularization. It is also found that the mutual information between the low and the high momentum modes shows different scaling behaviors when the effect of a cutoff becomes important.