Towards Jaffe and Taubes Conjectures in the strongly repulsive limit

Abstract

 We consider the abelian Yang-Mills-Higgs Action on all of ℝ² for large coupling constants (the strongly repulsive case). The homotopy classes of configurations are defined in a weak sense under the assumption of finite action only. We prove that the homotopy classes which admit a global minimizer for the YMH Action are exactly the +1, -1 and 0 degree classes. Finally we prove that any global minimizer in one of these homotopy classes is the axially symmetric solution (modulo gauge action) in the corresponding class.