Electrically charged finite energy solutions of an $SO(5)$ and an $SU(3)$ Higgs-Chern-Simons--Yang-Mills-Higgs systems in $3+1$ dimensions

TL;DR

This paper investigates finite energy, electrically charged solutions in $SO(5)$ and $SU(3)$ Higgs-Chern-Simons--Yang-Mills-Higgs models in 3+1 dimensions, revealing novel charge-energy relations and numerical solutions, including dyons with unique properties.

Contribution

It introduces new electrically charged solutions in Higgs-Chern-Simons-Yang-Mills-Higgs models with $SO(5)$ and $SU(3)$ gauge groups, highlighting their distinct charge and energy characteristics.

Findings

Solutions carry only electric charge or both electric and magnetic charges.

Electric charge contributions are significantly affected by Chern-Simons dynamics.

Masses of charged solutions can be smaller than neutral ones in certain parameter regions.

Abstract

We study spherically symmetric finite energy solutions of two Higgs-Chern-Simons--Yang-Mills-Higgs (HCS-YMH) models in $3+1$ dimensions, one with gauge group $SO(5)$ and the other with $SU(3)$. The Chern-Simons (CS) densities are defined in terms of both the Yang-Mills (YM) and Higgs fields and the choice of the two gauge groups is made so they do not vanish. The solutions of the $SO(5)$ model carry only electric charge and zero magnetic charge, while the solutions of the $SU(3)$ model are dyons carrying both electric and magnetic charges like the Julia-Zee (JZ) dyon. Unlike the latter however, the electric charge in both models receives an important contribution from the CS dynamics. We pay special attention to the relation between the energies and charges of these solutions. In contrast with the electrically charged JZ dyon of the Yang-Mills-Higgs (YMH) system, whose mass is larger than that of the electrically neutral (magnetic monopole) solutions, the masses of the electrically charged solutions of our HCS-YMH models can be smaller than their electrically neutral counterparts in some parts of the parameter space. To establish this is the main task of this work, which is performed by constructing the HCS-YMH solutions numerically. In the case of the $SU(3)$ HCS-YMH, we have considered the question of angular momentum, and it turns out that it vanishes.