Coexisting vortices and antivortices generated by dually gauged harmonic maps

In this paper, we first formulate a dually gauged harmonic map model, suggested from product Abelian Higgs field theory arising in impurity-inspired theories, and obtain new BPS system of equations governing coexisting vortices antivortices, which are topologically characterized by the Chern classes underlying Hermitian bundles Thom their associated dual bundles. We then establish existence uniqueness theorems for such vortices. For over compact surface, necessary sufficient conditions solutions. full plane, all finite-energy addition, also present precise expressions giving values various physical quantities solutions, including magnetic charges energies, terms total numbers two species coupling parameters involved.