Non-abelian instantons on a fuzzy four-sphere

TL;DR

This paper explores non-abelian instantons on a fuzzy four-sphere, identifying a non-commutative solution that extends classical SU(2) instantons and proposing a noncommutative Chern-Simons term.

Contribution

It introduces a non-commutative solution extending classical instantons on the fuzzy four-sphere and proposes a noncommutative second Chern class extension.

Findings

Identified a non-commutative solution to matrix model equations.

Extended the SU(2) instanton solution to the fuzzy four-sphere.

Proposed a noncommutative Chern-Simons term for higher-dimensional topology.

Abstract

We study the compatibility between the $BPST SU(2)$ instanton and the fuzzy four-sphere algebra. By using the projective module point of view as an intermediate step, we are able to identify a non-commutative solution of the matrix model equations of motion which minimally extends the SU(2) instanton solution on the classical sphere $S^4$. We also propose to extend the non-trivial second Chern class with the five-dimensional noncommutative Chern-Simons term.