Solutions to the Minimization Problem Arising in a Dark Monopole Model in Gauge Field Theory

Xiangqin Zhang, Yisong Yang

Published 2019-09-09Version 1

We prove the existence of dark monopole solutions in a recently formulated Yang--Mills--Higgs theory model with technical features similar to the classical monopole problems. The solutions are obtained as energy-minimizing static spherically symmetric field configurations of unit topological charge. We overcome the difficulty of recovering the full set of boundary conditions by a regularization method which may be applied to other more complicated problems concerning monopoles and dyons in non-Abelian gauge field theories. In a critical coupling situation, an explicit BPS solution is obtained, which may be used to provide energy estimates for non-BPS monopole solutions. In the limit of infinite Higgs coupling parameter, although no explicit construction is available, we establish an existence and uniqueness result for a monopole solution and obtain its energy bounds.