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Quantized Gauge Theory on the Fuzzy Sphere as Random Matrix Model

High Energy Physics - Theory 2008-11-26 v3 Mathematical Physics math.MP

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.

Keywords

Cite

@article{arxiv.hep-th/0307075,
  title  = {Quantized Gauge Theory on the Fuzzy Sphere as Random Matrix Model},
  author = {Harold Steinacker},
  journal= {arXiv preprint arXiv:hep-th/0307075},
  year   = {2008}
}

Comments

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

R2 v1 2026-07-22T15:18:05.839Z