Quantized Gauge Theory on the Fuzzy Sphere as Random Matrix Model

U(n) Yang-Mills theory on the fuzzy sphere S 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.