Entanglement Edge Modes of General Noncommutative Matrix Backgrounds

TL;DR

This paper investigates entanglement edge modes on noncommutative backgrounds from matrix quantum mechanics, revealing area law behavior on fuzzy spheres and a metric deformation akin to string theory frames.

Contribution

It demonstrates that nonlocal effects in noncommutative backgrounds can be resummed into a smooth metric deformation, extending understanding of entanglement in such geometries.

Findings

Area law behavior on fuzzy sphere edge modes

Nonlocal effects resummed into a metric deformation

Analogy to string and Einstein frame relationship

Abstract

We explore the structure of entanglement edge modes on noncommutative backgrounds that arise from matrix quantum mechanics. For the fuzzy sphere, despite nonlocality and UV/IR mixing, we find area law behavior in the dominant $U(N)$ representations governing the state of the edge modes. For general noncommutative backgrounds with no global symmetry, nonlocal effects resum into a smoothly varying coupling constant that deforms the metric to a different frame. The effect is analogous to the relationship between string frame and Einstein frame in string theory.