Supersymmetry and gauge invariance constraints in a U(1) x U(1)'-Higgs superconducting cosmic string model.

A supersymmetric extension of the U(1)× U(1)′-Higgs bosonic superconducting cosmic string model is considered, where the action is constructed from scalar chiral and vector superfields. The chiral superfields are assumed to transform separately under the Abelian gauge groups, 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)′ chiral superfield, the Witten mechanism for bosonic superconductivity (giving rise to long range gauge fields outside of the string) does not exist without the introduction of extra chiral supermultiplets. The simplest model that can accommodate the requisite interactions for a superconducting cosmic string solution with long range U(1) gauge fields requires five chiral supermultiplets. An investigation of the bosonic sector of this model indicates that a solution is admitted describing a gauge string surrounded by supersymmetric vacuum. By considering the effects of the gauge string background upon the remaining scalar fields of the theory, it is concluded that a parameter range exists for which the U(1) charged scalar fields condense within the core of the string, making it a superconducting string that can carry charge and/or current. It is also found that the neutral scalar field can be associated with particle bound states that are localized within or near the string core.