Exact monopole solutions in gauge theories for an arbitrary semisimple compact group

Abstract

We construct an exact n-parametric monopole and dyon solutions for an arbitrary compact gauge group G of rank n by using the symmetry between cylindrically symmetric instanton equations in Euclidean space R ₄ and monopole equations in Minkowski space R _3,1 (with Higgs scalar field in adjoint representation). The solutions are spherically symmetric with respect to the total momentum operator $- \overrightarrow {ir} \times \overrightarrow \nabla + \overrightarrow T , where \overrightarrow T$ represents the minimal embedding of SU(2) in G. Explicit expressions for the monopole magnetic charge and mass matrices are obtained. The remarkable aspect of our results is the existence of discrete series of the monopole solutions, which are labelled by n ‘quantum’ numbers and degenerated in the latter ones at a fixed monopole mass matrix.