A note on weak compactness of $\Omega$-Yang-Mills connections

TL;DR

This paper extends weak compactness results for Yang-Mills connections to a broader class called mbda-Yang-Mills connections on principal bundles over compact Riemannian manifolds, using a compensation compactness technique.

Contribution

It generalizes the weak continuity results from Yang-Mills fields to mbda-Yang-Mills connections on principal bundles over compact Riemannian manifolds.

Findings

Extended weak compactness to mbda-Yang-Mills connections.

Applied a compensation compactness argument by Chen and Giron.

Broadened understanding of gauge field compactness properties.

Abstract

In this note, applying a compensation compactness argument developped by Chen and Giron (arXiv.2108.13529) on Yang-Mills fields, we extends their weak continuity result to the more general class of $\Omega$-Yang-Mills connections on principle bundles over compact Riemannian manifold.