EXISTENCE AND UNIQUENESS OF BPS VACUUM AND MULTI-VORTICES IN INHOMOGENEOUS ABELIAN HIGGS MODEL

Abstract

The BPS limit of the inhomogeneous abelian Higgs model is considered in (1+2)-dimensions. The second order Bogomolny equation is examined in the presence of an inhomogeneity expressed as a function of spatial coordinates. Assuming a physically reasonable upper bound on the L-2 (R-2) norm of the inhomogeneity function, we prove the existence and uniqueness of nontrivial BPS vacuum solution of zero energy and topological BPS multi-vortex solutions of quantized positive energies.