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In this paper we study a system inspired on certain SUSY breaking models andon more recent Dark Matter scenarios. In our set-up, two Abelian gauge fieldsinteract via an operator that mixes their kinetic terms. We find the extendedSupersymmetric version of this system, that also generates a Higgs portal typeof interaction. We obtain and study both analytically and numerically, theequations defining topologically stable string-like objects. We check ourresults using two different approaches. Various technical details areexplicitly stated for the benefit of various readers.

N=2 SUSY Abelian Higgs model with hidden sector and BPS equations