Isolated singularities of 3-dimensional Yang-Mills-Higgs fields

TL;DR

This paper investigates the behavior of 3-dimensional Yang-Mills-Higgs fields near isolated singularities, providing decay estimates and conditions under which singularities can be removed, thus extending classical results in gauge theory.

Contribution

It introduces decay estimates and removable singularity theorems for 3d Yang-Mills-Higgs fields, generalizing previous results for Yang-Mills fields and harmonic maps.

Findings

Decay estimates near isolated singularities

Removable singularity theorems under energy conditions

Generalization of classical singularity results

Abstract

In this paper, we derive decay estimates near isolated singularities of 3-dimensional (3d) Yang-Mills-Higgs fields defined on a fiber bundle, where the fiber space is a compact Riemannian manifold and the structure group is a connected compact Lie group. As an application, we obtain removable singularity theorems for 3d Yang-Mills-Higgs fields under different types of energy conditions, which generalizes classical removable singularity theorems for 3d Yang-Mills fields~\cite{S84,SS84} and 3d harmonic maps~\cite{L85}.