Noncommutative Gauge Theories on Fuzzy Sphere and Fuzzy Torus from Matrix Model

TL;DR

This paper explores noncommutative gauge theories on fuzzy sphere and torus derived from a matrix model of Yang-Mills theory, analyzing their properties through large N limits and classical solutions.

Contribution

It introduces a matrix model with classical solutions representing fuzzy sphere and torus, enabling the study of noncommutative gauge theories on these manifolds.

Findings

Classical solutions exist for finite matrix sizes.

Gauge theories are derived by expanding around these solutions.

Large N limits reveal behaviors of gauge invariant operators.

Abstract

We consider a reduced model of four-dimensional Yang-Mills theory with a mass term. This matrix model has two classical solutions, two-dimensional fuzzy sphere and two-dimensional fuzzy torus. These classical solutions are constructed by embedding them into three or four dimensional flat space. They exist for finite size matrices, that is, the number of the quantum on these manifolds is finite. Noncommutative gauge theories on these noncommutative manifolds are derived by expanding the model around these classical solutions and studied by taking two large $N$ limits, a commutative limit and a large radius limit. The behaviors of gauge invariant operators are also discussed.