Quantized Gauge Theory on the Fuzzy Sphere as Random Matrix Model

TL;DR

This paper quantizes U(n) Yang-Mills theory on the fuzzy sphere using random matrix models, enabling explicit calculation of the partition function and monopole solutions, and connecting to classical sphere results in the large N limit.

Contribution

It introduces a matrix model formulation for gauge theory on the fuzzy sphere, facilitating analytical evaluation of the partition function and monopole solutions.

Findings

Partition function reduces to eigenvalue integral for large N

Classical sphere results recovered in the large N limit

Explicit monopole solutions are obtained

Abstract

U(n) Yang-Mills theory on the fuzzy sphere S^2_N is quantized using random matrix methods. The gauge theory is formulated as a matrix model for a single Hermitian matrix subject to a constraint, and a potential with two degenerate minima. This allows to reduce the path integral over the gauge fields to an integral over eigenvalues, which can be evaluated for large N. The partition function of U(n) Yang-Mills theory on the classical sphere is recovered in the large N limit, as a sum over instanton contributions. The monopole solutions are found explicitly.