Comments on the Entanglement Entropy on Fuzzy Spaces

TL;DR

This paper investigates how entanglement entropy in 2+1 fuzzy models is primarily determined by near boundary degrees of freedom, providing analytical and numerical support for an area law in these noncommutative spaces.

Contribution

It identifies the near boundary degrees of freedom as key to entanglement entropy and derives the area law analytically using a $1/N$ expansion in fuzzy models.

Findings

Entropy is stored in near boundary degrees of freedom

Analytical derivation of the area law using $1/N$ expansion

Numerical evidence supports the near boundary approximation

Abstract

We locate the relevant degrees of freedom for the entanglement entropy on some 2+1 fuzzy models. It is found that the entropy is stored in the near boundary degrees of freedom. We give a simple analytical derivation for the area law using $1/N$ like expansion when only the near boundary degrees of freedom are incorporated. Numerical and qualitative evidences for the validity of near boundary approximation are finally given .