Noncommutative Gauge Theory on Fuzzy Sphere from Matrix Model

Abstract

We derive a noncommutative U(1) and U(n) gauge theory on the fuzzy sphere from a three dimensional matrix model by expanding the model around a classical solution of the fuzzy sphere. Chern-Simons term is added in the matrix model to make the fuzzy sphere as a classical solution of the model. Majorana mass term is also added to make it supersymmetric. We consider two large $N$ limits, one corresponding to a gauge theory on a commutative sphere and the other to that on a noncommutative plane. We also investigate stability of the fuzzy sphere by calculating one-loop effective action around classical solutions. In the final part of this paper, we consider another matrix model which gives a supersymmetric gauge theory on the fuzzy sphere. In this matrix model, only Chern-Simons term is added and supersymmetry transformation is modified.

31 pages, more investigations of the theory in the commutative limit and references added

References in corpus (2)

• D-brane Solutions in Non-Commutative Gauge Theory on Fuzzy Sphere
• Normalized Weyl-type $\star$-product on Kähler manifolds

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