We propose a theoretical framework for $R$-parity violation. It is realized by a class of Calabi-Yau compactification of heterotic string theory. Trilinear $R$-parity violation in superpotential is either absent or negligibly small without an unbroken symmetry, due to a selection rule based on charge counting of a spontaneously broken U(1) symmetry. Although such a selection rule cannot be applied in general to nonrenormalizable operators in the low-energy effective superpotential, it is valid for terms trilinear in low-energy degrees of freedom, and hence can be used as a solution to the dimension-4 proton decay problem in the minimal supersymmetric standard model. Bilinear $R$-parity violation is generated, but there are good reasons why it is small enough to satisfy its upper bounds from neutrino mass and washout of baryon/lepton asymmetry. All $R$-parity violating dimension-5 operators can be generated. In this theoretical framework, nucleons can decay through squark-exchange diagrams combining dimension-5 and bilinear $R$-parity violating operators. $B-L$ breaking neutron decay is predicted.

• Received 9 November 2008

DOI:https://doi.org/10.1103/PhysRevD.79.075002