Noncommutative Gauge Theory on Fuzzy Sphere from Matrix Model

TL;DR

This paper derives noncommutative gauge theories on the fuzzy sphere from matrix models, explores their large N limits, and investigates their stability and supersymmetric extensions.

Contribution

It introduces a matrix model framework for gauge theories on fuzzy spheres, including supersymmetric versions with Chern-Simons terms, and analyzes their stability and large N limits.

Findings

Successful derivation of gauge theories on fuzzy sphere from matrix models

Analysis of stability via one-loop effective action

Construction of supersymmetric gauge theories on fuzzy sphere

Abstract

We derive a noncommutative U(1) and U(n) gauge theory on the fuzzy sphere from a three dimensional matrix model by expanding the model around a classical solution of the fuzzy sphere. Chern-Simons term is added in the matrix model to make the fuzzy sphere as a classical solution of the model. Majorana mass term is also added to make it supersymmetric. We consider two large $N$ limits, one corresponding to a gauge theory on a commutative sphere and the other to that on a noncommutative plane. We also investigate stability of the fuzzy sphere by calculating one-loop effective action around classical solutions. In the final part of this paper, we consider another matrix model which gives a supersymmetric gauge theory on the fuzzy sphere. In this matrix model, only Chern-Simons term is added and supersymmetry transformation is modified.