An $L^{2}$-isolation theorem for Yang-Mills fields on K\"{a}hler surfaces

TL;DR

This paper establishes an $L^{2}$ energy gap theorem for Yang-Mills connections on Kähler surfaces with positive scalar curvature, extending results to Calabi-Yau 2-folds, advancing understanding of gauge theory in complex geometry.

Contribution

It introduces an $L^{2}$-isolation theorem for Yang-Mills fields on Kähler surfaces and Calabi-Yau 2-folds, providing new energy gap results in these geometric settings.

Findings

Proves an $L^{2}$ energy gap for Yang-Mills connections on Kähler surfaces.

Extends energy gap results to Calabi-Yau 2-folds.

Provides conditions under which Yang-Mills connections are trivial or flat.

Abstract

We prove an $L^{2}$ energy gap result for Yang-Mills connections on principal $G$-bundles over compact K\"{a}hler surfaces with positive scalar curvature. We prove related results for compact simply-connected Calabi-Yau $2$-folds.