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arXiv · hep-th/0503041

Gauge Theory on Fuzzy S^2 x S^2 and Regularization on Noncommutative R^4

Wolfgang Behr·Frank Meyer·Harold Steinacker
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Abstract

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 commutative limit N -> infinity. The model can be used as a regularization of gauge theory on noncommutative R^4_θin a particular scaling limit, which is studied in detail. We also find topologically non-trivial U(1) solutions, which reduce to the known "fluxon" solutions in the limit of R^4_θ, reproducing their full moduli space. Other solutions which can be interpreted as 2-dimensional branes are also found. The quantization of the model is defined non-perturbatively in terms of a path integral which is finite. A gauge-fixed BRST-invariant action is given as well. Fermions in the fundamental representation of the gauge group are included using a formulation based on SO(6), by defining a fuzzy Dirac operator which reduces to the standard Dirac operator on S^2 x S^2 in the commutative limit. The chirality operator and Weyl spinors are also introduced.

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Wolfgang Behr, Frank Meyer, Harold Steinacker. 2005-05-24. Gauge Theory on Fuzzy S^2 x S^2 and Regularization on Noncommutative R^4. https://doi.org/10.1088/1126-6708%2F2005%2F07%2F040

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