A Duality for Yang-Mills Moduli Spaces on Noncommutative Manifolds

TL;DR

This paper establishes a duality between Yang-Mills moduli spaces on noncommutative manifolds and their dual modules, providing new insights into their structure and computing specific examples without traditional methods.

Contribution

It proves a homeomorphism between moduli spaces on noncommutative flows and their duals, extending to multiflows, and computes instanton moduli spaces on noncommutative Euclidean space.

Findings

Moduli spaces are homeomorphic on dual noncommutative flows.

Computed instanton moduli spaces on noncommutative Euclidean 4-space.

Extended duality results to multiflows.

Abstract

Studied are the moduli spaces of Yang-Mills connections on finitely generated projective modules associated with noncommutative flows. It is actually shown that they are homeomorphic to those on the dual modules associated with the dual noncommutative flows. Moreover the result is also affirmative in the case of multiflows. As an important application, computed are the moduli spaces of the instanton bundles over the noncommutative Euclidean 4-space with respect to the canonical action of space translations without using the ADHM-construction.