Entanglement Entropy on Fuzzy Spaces

TL;DR

This paper investigates entanglement entropy in 2+1 dimensional fuzzy spaces, revealing proportionality to boundary degrees of freedom and IR-UV mixing effects, with finite entropy for finite ignored regions.

Contribution

It provides numerical evaluation of entanglement entropy on fuzzy spheres and discs, highlighting boundary proportionality and divergence behavior in the Moyal limit.

Findings

Entanglement entropy proportional to boundary degrees of freedom.

Divergence of entropy per unit area in the Moyal limit for infinite regions.

Finite entropy expected for finite ignored regions on non-commutative spaces.

Abstract

We study the entanglement entropy of a scalar filed in 2+1 spacetime where space is modeled by a fuzzy sphere and a fuzzy disc. In both models we evaluate numerically the resulting entropies and find that they are proportional to the number of boundary degrees of freedom. In the Moyal plan limit of the fuzzy disc the entanglement entropy per unit area (length) diverges if the ignored region is of infinite size. The divergence is (interpreted) of IR-UV mixing origin. In general we expect the entanglement entropy per unit area to be finite on a non-commutative space if the ignored region is of finite size.