Quantized Gauge Theory on the Fuzzy Sphere as Random Matrix Model

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.

36 pages, 1 figure. Minor clarifications, typos corrected. To appear in Nucl.Phys.B

References in corpus (3)

• Power-counting theorem for non-local matrix models and renormalisation
• Lectures on Two-Dimensional Noncommutative Gauge Theory 2: Quantization
• Algebraic brane dynamics on SU(2): excitation spectra

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