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We define U(n) gauge theory on fuzzy S^2_N x S^2_N as a multi-matrix model,which reduces to ordinary Yang-Mills theory on S^2 x S^2 in the commutativelimit N -> infinity. The model can be used as a regularization of gauge theoryon noncommutative R^4_\theta in a particular scaling limit, which is studied indetail. We also find topologically non-trivial U(1) solutions, which reduce tothe known "fluxon" solutions in the limit of R^4_\theta, reproducing their fullmoduli space. Other solutions which can be interpreted as 2-dimensional branesare also found. The quantization of the model is defined non-perturbatively interms of a path integral which is finite. A gauge-fixed BRST-invariant actionis given as well. Fermions in the fundamental representation of the gauge groupare included using a formulation based on SO(6), by defining a fuzzy Diracoperator which reduces to the standard Dirac operator on S^2 x S^2 in thecommutative limit. The chirality operator and Weyl spinors are also introduced.Comment: 39 pages. V2-4: References added, typos fixe

Gauge theory on fuzzyS2×S2and regularization on noncommutative Bbb R4

Gauge theory on fuzzyS²×S²and regularization on noncommutative Bbb R⁴