Non-generic couplings in supersymmetric standard models

We study two phases of a heterotic standard model, obtained from a Calabi–Yau compactification of the E8×E8E8×E8 heterotic string, in the context of the associated four-dimensional effective theories. In the first phase we have a standard model gauge group, an MSSM spectrum, four additional U(1)U(1) symmetries and singlet fields. In the second phase, obtained from the first by continuing along the singlet directions, three of the additional U(1)U(1) symmetries are spontaneously broken and the remaining one is a B–L   symmetry. In this second phase, dimension five operators inducing proton decay are consistent with all symmetries and as such, they are expected to be present. We show that, contrary to this expectation, these operators are forbidden due to the additional U(1)U(1) symmetries present in the first phase of the model. We emphasise that such “unexpected” absences of operators, due to symmetry enhancement at specific loci in the moduli space, can be phenomenologically relevant and, in the present case, protect the model from fast proton decay.