  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 in the
simplest vacua in this context. The electroweak phase transition also disallows
fermion superconductivity, although substantial bound state fermion currents
can exist.
