Localization for Yang-Mills Theory on the Fuzzy Sphere

Details Localization for Yang-Mills Theory on the Fuzzy Sphere Localization for Yang-Mills Theory on the Fuzzy Sphere

2007-01-05

arxiv.org/abs/hep-th/0701041v3

Commun.Math.Phys.278:193-252,2008

Physics

High Energy Physics

High Energy Physics - Theory

55 pages. V2: references added; V3: minor corrections, reference added; Final version to be published in Communications in Mat

Scientific paper

10.1007/s00220-007-0386-0

We present a new model for Yang-Mills theory on the fuzzy sphere in which the configuration space of gauge fields is given by a coadjoint orbit. In the classical limit it reduces to ordinary Yang-Mills theory on the sphere. We find all classical solutions of the gauge theory and use nonabelian localization techniques to write the partition function entirely as a sum over local contributions from critical points of the action, which are evaluated explicitly. The partition function of ordinary Yang-Mills theory on the sphere is recovered in the classical limit as a sum over instantons. We also apply abelian localization techniques and the geometry of symmetric spaces to derive an explicit combinatorial expression for the partition function, and compare the two approaches. These extend the standard techniques for solving gauge theory on the sphere to the fuzzy case in a rigorous framework.

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