A Chern–Simons–Yang–Mills–Higgs system in 3+1 dimensions

Abstract

We study spherically symmetric solutions of an SO(5) Chern–Simons–Yang–Mills–Higgs system in 3+1 dimensions. The Chern–Simons densities are defined in terms of both Yang–Mills fields and a five-component isomultiplet Higgs. The SO(3) × SO(2) solutions are analyzed in a systematic way, by employing numerical methods. These finite energy configurations possess both electric and magnetic global charges, differing radically, however, from Julia–Zee dyons. When two or more of these Chern–Simons densities are present in the Lagrangian, solutions with vanishing electric charge but nonvanishing electrostatic potential may exist.