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

TL;DR

This paper demonstrates a mechanism for the dynamical generation of a nontrivial index on the fuzzy 2-sphere by analyzing the stability and decay of monopole configurations within a matrix model, extending previous topological charge studies.

Contribution

It introduces a new mechanism for the dynamical generation of a nontrivial index on the fuzzy 2-sphere through stability analysis of monopole configurations in a matrix model.

Findings

TP monopole configuration is more stable than the pure gauge theory.

The mechanism allows for the dynamical emergence of topological indices.

Analysis of decay processes clarifies stability conditions.

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.