Gauge Theory on Fuzzy S^2 x S^2 and Regularization on Noncommutative R^4
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_\theta in 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_\theta, 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.
Keywords
Cite
@article{arxiv.hep-th/0503041,
title = {Gauge Theory on Fuzzy S^2 x S^2 and Regularization on Noncommutative R^4},
author = {Wolfgang Behr and Frank Meyer and Harold Steinacker},
journal= {arXiv preprint arXiv:hep-th/0503041},
year = {2009}
}
Comments
39 pages. V2-4: References added, typos fixed