Electrically and magnetically charged vortices in the Chern-Simons-Higgs theory

In this paper, we prove the existence of finite-energy electrically and magnetically charged vortex solutions in the full Chern-Simons-Higgs theory, for which both the Maxwell term and the Chern-Simons term are present in the Lagrangian density. We consider both Abelian and non-Abelian cases. The solutions are smooth and satisfy natural boundary conditions. Existence is established via a constrained minimization procedure applied on indefinite action functionals. This work settles a long-standing open problem concerning the existence of dually charged vortices in the classical gauge field Higgs model minimally extended to contain a Chern-Simons term.