Ginsparg-Wilson Relation and 't Hooft-Polyakov Monopole on Fuzzy 2-Sphere

TL;DR

This paper explores Ginsparg-Wilson fermions on fuzzy 2-spheres, analyzing chiral anomalies, topological charges, and monopole configurations, confirming their correct classical limits and extending understanding of noncommutative geometry in gauge theories.

Contribution

It demonstrates the correct commutative limit of chiral anomalies and monopole configurations within the fuzzy 2-sphere framework, advancing noncommutative gauge theory understanding.

Findings

Chiral anomaly reduces to the Chern character in the commutative limit.

Fuzzy 2-sphere monopoles have correct classical limits.

General configurations are successfully incorporated.

Abstract

We investigate several properties of Ginsparg-Wilson fermion on fuzzy 2-sphere. We first examine chiral anomaly up to the second order of the gauge field and show that it is indeed reduced to the correct form of the Chern character in the commutative limit. Next we study topologically non-trivial gauge configurations and their topological charges. We investigate 't Hooft-Polyakov monopole type configuration on fuzzy 2-sphere and show that it has the correct commutative limit. We also consider more general configurations in our formulation.