Supersymmetry and Gauge Invariance Constraints in a U(1)$\times $U(1)$^{\prime }$-Higgs Superconducting Cosmic String Model

Abstract

A supersymmetric extension of the $U(1)\times U(1)^{\prime }$-Higgs bosonic superconducting cosmic string model is considered,and the constraints imposed upon such a model due to renormalizability, supersymmetry, and gauge invariance are examined. For a simple model with a single $U(1)$ chiral superfield and a single $% U(1)^{\prime }$ chiral superfield, the Witten mechanism for bosonic superconductivity (giving rise to long range gauge fields outside of the string) does not exist. The simplest model that can accommodate the requisite interactions requires five chiral supermultiplets. This superconducting cosmic string solution is investigated.