U(2) projectors and 't Hooft-Polyakov monopoles on a fuzzy sphere

TL;DR

This paper extends a method for deriving noncommutative monopoles on fuzzy spheres to non-abelian cases, exploring deformations of the Chern class in non-commutative geometry.

Contribution

It generalizes a projective module and matrix model approach to non-abelian monopoles on fuzzy spheres, recovering known results and proposing a deformation of the Chern class.

Findings

Successful extension to non-abelian monopoles

Recovery of known noncommutative monopole results

Proposal for deforming the Chern class in non-commutative geometry

Abstract

We show how to generalize our method, based on projective modules and matrix models, which enabled us to derive noncommutative monopoles on a fuzzy sphere, to the non-abelian case, recovering known results in literature. We then discuss a possible candidate for deforming the commutative Chern class to the non-commutative case.