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

Abstract

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.

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

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• Dynamical generation of fuzzy extra dimensions, dimensional reduction and symmetry breaking
• Embedding of theories with SU(2|4) symmetry into the plane wave matrix model
• Fermions on spontaneously generated spherical extra dimensions
• Fiber Bundles and Matrix Models
• Ginsparg-Wilson Dirac operator in the monopole backgrounds on the fuzzy 2-sphere
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Cited by in corpus (2)

• Finite-matrix formulation of gauge theories on a non-commutative torus with twisted boundary conditions
• Ginsparg-Wilson relation on a fuzzy 2-sphere for adjoint matter