Entanglement entropy on a fuzzy sphere with a UV cutoff

TL;DR

This paper studies how a UV cutoff affects entanglement entropy in a noncommutative fuzzy sphere, revealing a transition from extensive to area-law behavior and confirming holographic features.

Contribution

It introduces a UV cutoff in scalar field theory on a fuzzy sphere and analyzes its impact on entanglement entropy and nonlocality.

Findings

Entanglement entropy is extensive for small regions below the nonlocality scale.

For larger regions, entanglement entropy follows an area law.

Mutual information remains unaffected by the UV cutoff.

Abstract

We introduce a UV cutoff into free scalar field theory on the noncommutative (fuzzy) two-sphere. Due to the IR-UV connection, varying the UV cutoff allows us to control the effective nonlocality scale of the theory. In the resulting fuzzy geometry, we establish which degrees of freedom lie within a specific geometric subregion and compute the associated vacuum entanglement entropy. Entanglement entropy for regions smaller than the effective nonlocality scale is extensive, while entanglement entropy for regions larger than the effective nonlocality scale follows the area law. This reproduces features previously obtained in the strong coupling regime through holography. We also show that mutual information is unaffected by the UV cutoff.