Gauge Theory on Noncommutative Supersphere from Supermatrix Model

TL;DR

This paper constructs a supermatrix model that describes gauge theory on a noncommutative supersphere, revealing supersymmetry and gauge symmetry properties, and explores its commutative limit.

Contribution

It introduces a novel supermatrix model with a classical solution representing a fuzzy supersphere, enabling gauge theory formulation on noncommutative superspaces.

Findings

Model exhibits $osp(1|2)$ supersymmetry.

Gauge symmetry is $u(2L+1|2L)$.

Discusses a commutative limit with fixed supersphere radius.

Abstract

We construct a supermatrix model which has a classical solution representing the noncommutative (fuzzy) two-supersphere. Expanding supermatrices around the classical background, we obtain a gauge theory on a noncommutative superspace on sphere. This theory has $osp(1|2)$ supersymmetry and $u(2L+1|2L)$ gauge symmetry. We also discuss a commutative limit of the model keeping radius of the supersphere fixed.