We study isolated singularities of two dimensional Yang-Mills-Higgs fields defined on a fiber bundle, where the fiber space is a compact Riemannian manifold and the structure group is a compact connected Lie group. In general the singularity can not be removed due to possibly non-vanishing limit holonomy around the singular points. We establish a sharp asymptotic decay estimate of the Yang-Mills-Higgs field near a singular point, where the decay rate is precisely determined by the limit holonomy. Our result can be viewed as a generalization of the classical removable singularity theorem of two dimensional harmonic maps.

中文翻译：

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表面杨-米尔斯-希格斯场的孤立奇点

我们研究定义在纤维丛上的二维杨-米尔斯-希格斯场的孤立奇点，其中纤维空间是一个紧凑的黎曼流形，结构群是一个紧密相连的李群。通常，由于奇点周围可能存在非消失极限完整，奇点无法去除。我们建立了一个奇异点附近的 Yang-Mills-Higgs 场的急剧渐近衰减估计，其中衰减率由极限完整学精确确定。我们的结果可以看作是二维调和映射的经典可移除奇点定理的推广。