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

TL;DR

This paper proves the existence of dark monopole solutions in a Yang--Mills--Higgs model, introducing a regularization method to handle boundary conditions and analyzing solutions in various coupling regimes.

Contribution

It establishes existence, uniqueness, and energy bounds for dark monopoles in a gauge theory, employing a novel regularization approach and BPS solutions.

Findings

Existence of dark monopole solutions proven.

Regularization method for boundary conditions introduced.

Energy bounds established for monopoles in different regimes.

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.