Moduli spaces of noncommutative instantons: gauging away noncommutative parameters

TL;DR

This paper advances the understanding of noncommutative instanton moduli spaces by constructing gauge-invariant parameter spaces within a braided monoidal category framework, enabling classical descriptions from noncommutative parameters.

Contribution

It introduces a method to define and analyze noncommutative parameter spaces for instantons and demonstrates how to gauge away noncommutative parameters to recover classical moduli spaces.

Findings

Constructed noncommutative families of instantons on deformed spheres.

Developed a noncommutative quotient to remove gauge parameters.

Showed classical parameter spaces can be recovered from noncommutative ones.

Abstract

Using the theory of noncommutative geometry in a braided monoidal category, we improve upon a previous construction of noncommutative families of instantons of arbitrary charge on the deformed sphere S^4_\theta. We formulate a notion of noncommutative parameter spaces for families of instantons and we explore what it means for such families to be gauge equivalent, as well as showing how to remove gauge parameters using a noncommutative quotient construction. Although the parameter spaces are a priori noncommutative, we show that one may always recover a classical parameter space by making an appropriate choice of gauge transformation.