B-L cosmic strings in heterotic standard models

E-8 x E-8 heterotic string and M-theory, when compactified on smooth Calabi-Yau manifolds with SU(4) vector bundles, can give rise to softly broken N = 1 supersymmetric theories with the exact matter spectrum of the MSSM, including three right-handed neutrinos and one Higgs-Higgs conjugate pair of supermultiplets. These vacua have the SU(3)(C) x SU(2)(L) x U(1)(Y) gauge group of the standard model augmented by an additional gauged U(1) B L. Their minimal content requires that the B-L symmetry be spontaneously broken by a vacuum expectation value of at least one right-handed sneutrino. The soft supersymmetry breaking operators can induce radiative breaking of the B-L gauge symmetry with an acceptable B-L/electroweak hierarchy. In this paper, it is shown that U(1) B L cosmic strings occur in this context, potentially with both bosonic and fermionic superconductivity. We present a numerical analysis that demonstrates that boson condensates can, in principle, form for theories of this type. However, the weak Yukawa and gauge couplings of the right-handed sneutrino suggests that bosonic superconductivity will not occur the simplest vacua in this context. The electroweak phase transition also disallows superconductivity, although substantial bound state fermion currents can exist.