Dynamical generation of a nontrivial index on the fuzzy 2-sphere

Abstract

In the previous paper hep-th/0312199 we studied the 't Hooft-Polyakov (TP) monopole configuration in the U(2) gauge theory on the fuzzy 2-sphere and showed that it has a nonzero topological charge in the formalism based on the Ginsparg-Wilson relation. In this paper, by showing that the TP monopole configuration is stabler than the U(2) gauge theory without any condensation in the Yang-Mills-Chern-Simons matrix model, we will present a mechanism for dynamical generation of a nontrivial index. We further analyze the instability and decay processes of the U(2) gauge theory and the TP monopole configuration.

Latex2e, 30 pages, 4 figures, the topological charge for a monopole configuration is corrected, reference added, the final version to appear in Physical Review D (the typos mentioned in the erratum are corrected)

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• Ginsparg-Wilson Relation and 't Hooft-Polyakov Monopole on Fuzzy 2-Sphere
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• On the fermion spectrum of spontaneously generated fuzzy extra dimensions with fluxes
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• Perturbative versus nonperturbative dynamics of the fuzzy S^2*S^2
• Ginsparg-Wilson Dirac operator in the monopole backgrounds on the fuzzy 2-sphere
• Impact of supersymmetry on the nonperturbative dynamics of fuzzy spheres
• Higher-Dimensional Unified Theories with Fuzzy Extra Dimensions
• The index of the overlap Dirac operator on a discretized 2d non-commutative torus
• Probability distribution of the index in gauge theory on 2d non-commutative geometry
• Index theorem in spontaneously symmetry-broken gauge theories on a fuzzy 2-sphere
• Finite-matrix formulation of gauge theories on a non-commutative torus with twisted boundary conditions
• Admissibility Condition and Nontrivial Indices on a Noncommutative Torus
• Probability of the Standard Model Appearance from a Matrix Model
• Fuzzy Extra Dimensions: Dimensional Reduction, Dynamical Generation and Renormalizability
• Unified Gauge Theories and Reduction of Couplings: from Finiteness to Fuzzy Extra Dimensions
• Construction of a topological charge on fuzzy S^2 x S^2 via Ginsparg-Wilson relation
• Dominance of a single topological sector in gauge theory on non-commutative geometry
• Ginsparg-Wilson relation on a fuzzy 2-sphere for adjoint matter
• The instability of intersecting fuzzy spheres
• Probability distribution over some phenomenological models in the matrix model compactified on a torus
• Dirac operator on the quantum fuzzy four-sphere $S_{qF}^4$
• Fuzzy AdS-conifold $Y_{Ad{S}_F}^6$ and Dirac operator of principal fibration $X_{Ad{S}_F}^5\to Ad{S}_F^2\times Ad{S}_F^2$