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arXiv · 1909.03864

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

Xiangqin Zhang·Yisong Yang
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Abstract

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. Furthermore we show in a critical coupling situation that an explicit BPS solution may be used to provide energy estimates for non-BPS monopole solutions. Besides, 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.

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Xiangqin Zhang, Yisong Yang. 2019-09-09. Solutions to the Minimization Problem Arising in a Dark Monopole Model in Gauge Field Theory. https://doi.org/10.1016/j.nuclphysb.2019.114851

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