Solutions to the minimization problem arising in a dark monopole model in gauge field theory

Xiangqin Zhang, Yisong Yang

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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.

Original languageEnglish (US)
Article number114851
JournalNuclear Physics B
StatePublished - Feb 2020


ASJC Scopus subject areas

  • Nuclear and High Energy Physics

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