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.

Comments: 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)