Lepton number violation in supersymmetric grand unified theories

We argue that the nature of the global conservation laws in Supersymmetric Grand Unified Theories is determined by the basic vacuum configuration in t he model rather than its Lagrangian. It is shown that the suppression of ba ryon number violation in a general (R-parity violating) superpotential can naturally appear in some extended SU(N) SUSY GUTs which, among other degene rate symmetry-breaking vacua, have a missing VEV vacuum configuration givin g a solution to the doublet-triplet splitting problem. We construct SU(7) a nd SU(8) GUTs where the effective lepton number violating couplings immedia tely evolve, while the baryon number non-conserving ones are safely project ed out as the GUT symmetry breaks down to that of the MSSM. However at the next stage, when SUSY breaks, the radiative corrections shift the missing V EV components to some nonzero values of order M-SUSY, thereby inducing the ordinary Higgs doublet mass, on the one hand, and tiny baryon number violat ion, on the other. So, a missing VEV solution to the gauge hierarchy proble m leads at the same time to a similar hierarchy of baryon vs lepton number violation. (C) 2000 Elsevier Science B.V. All rights reserved.