Dyons and Magnetic Monopoles Revisited

TL;DR

This paper constructs and analyzes dyon solutions in SU(N) and G2 gauge theories, revealing their properties, mass insensitivity to potential coupling, and the existence of two distinct dyon types in G2 under SU(3) subgroup.

Contribution

It introduces a method for constructing dyons in SU(N) and G2, demonstrating their properties and the conditions for their existence, including a novel classification of dyons in G2.

Findings

Dyon mass is insensitive to the Higgs potential coupling mbda.

Dyons in G2 exist only under the SU(3) subgroup.

Two types of dyons are identified in G2, with one resembling SU(3) dyons and another with atypical magnetic charge.

Abstract

We construct dyon solutions in SU(N) with topological electric and magnetic charge. Assuming a |\Phi|^4-like potential for the Higgs field we show that the mass of the dyons is relatively insensitive to the coupling parameter \lambda characterizing the potential. We then apply the methodology of constructing dyon solutions in SU(N) to G2. In order to define the electromagnetic field consistently in the manner that we propose we find that dyon solutions exist only when G2 is considered under the action of its maximal and regular subgroup SU(3). In this case we find two different types of dyons, one of which has properties identical to dyons in SU(3). The other dyon has some properties which are seemingly atypical, e.g. the magnetic charge g_m = 4 \pi 3/e, which differs from the 't Hooft/Polyakov monopole where g_m = 4 \pi 1/e.