Projectors, matrix models and noncommutative instantons

TL;DR

This paper explores the relationship between projectors, matrix models, and noncommutative instantons on fuzzy four-spheres, revealing the physical implications of noncommutative topology and extending to the U(2) case related to classical instantons.

Contribution

It deconstructs finite projective modules for the fuzzy four-sphere and connects them with matrix models, highlighting noncommutative topological features and their physical significance.

Findings

Correlated projectors with matrix models on fuzzy four-sphere

Identified noncommutative topological implications in the model

Extended analysis to U(2) case related to classical instantons

Abstract

We deconstruct the finite projective modules for the fuzzy four-sphere, described in a previous paper, and correlate them with the matrix model approach, making manifest the physical implications of noncommutative topology. We briefly discuss also the U(2) case, being a smooth deformation of the celebrated BPST SU(2) classical instantons on a sphere.