Index theorem in spontaneously symmetry-broken gauge theories on a fuzzy 2-sphere

Details Index theorem in spontaneously symmetry-broken gauge theories on a fuzzy 2-sphere Index theorem in spontaneously symmetry-broken gauge theories on a fuzzy 2-sphere

2008-04-03

arxiv.org/abs/0804.0568v2

Phys.Rev.D78:025028,2008

Physics

High Energy Physics

High Energy Physics - Theory

37 pages, 3 figures, typo corrected, version published in Physical Review D

Scientific paper

10.1103/PhysRevD.78.025028

We consider a gauge-Higgs system on a fuzzy 2-sphere and study the topological structure of gauge configurations, when the U(2) gauge symmetry is spontaneously broken to U(1) times U(1) by the vev of the Higgs field. The topology is classified by the index of the Dirac operator satisfying the Ginsparg-Wilson relation, which turns out to be a noncommutative analog of the topological charge introduced by 't Hooft. It can be rewritten as a form whose commutative limit becomes the winding number of the Higgs field. We also study conditions which assure the validity of the formulation, and give a generalization of the admissibility condition. Finally we explicitly calculate the topological charge of a one-parameter family of configurations.

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