Fuzzy Non-Trivial Gauge Configurations

TL;DR

This paper explores the construction of non-trivial gauge configurations like monopoles and solitons on fuzzy spheres using noncommutative geometry, highlighting finite-dimensional matrix models and topological charge calculations.

Contribution

It introduces a method to construct and analyze monopoles and solitons on fuzzy spheres via K-theory and cyclic cohomology, advancing discrete noncommutative physics.

Findings

Construction of monopoles and solitons on fuzzy ${f S}^2$

Finite-dimensional matrix models for gauge configurations

Calculation of topological charges using noncommutative geometry

Abstract

In this talk we will report on few results of discrete physics on the fuzzy sphere . In particular non-trivial field configurations such as monopoles and solitons are constructed on fuzzy ${\bf S}^2$ using the language of K-theory, i.e projectors . As we will show, these configurations are intrinsically finite dimensional matrix models . The corresponding monopole charges and soliton winding numbers are also found using the formalism of noncommutative geometry and cyclic cohomology .