Two-Dimensional Gauge Theory and Matrix Model

TL;DR

This paper explores a matrix model derived from Chern-Simons theory on S^3, revealing its decomposition into sectors related to SU(2) representations and its connection to SU(N) Yang-Mills theory on S^2 in the large matrix limit.

Contribution

It demonstrates how a dimensionally reduced Chern-Simons matrix model decomposes into sectors and reproduces Yang-Mills theory on S^2 as the matrix size increases.

Findings

Matrix integration decomposes into SU(2) representation sectors.

N-block sectors reproduce SU(N) Yang-Mills on S^2.

The model links Chern-Simons theory to Yang-Mills theory via matrix models.

Abstract

We study a matrix model obtained by dimensionally reducing Chern-Simon theory on S^3. We find that the matrix integration is decomposed into sectors classified by the representation of SU(2). We show that the N-block sectors reproduce SU(N) Yang-Mills theory on S^2 as the matrix size goes to infinity.