  The fate of R-parity is one of the central issues in the minimal
supersymmetric standard model (MSSM). Gauged $B-L$ symmetry provides a natural
framework for addressing this question. Recently, it was pointed out that the
minimal such theory does not need any additional Higgs if the $B-L$ breaking is
achieved through the VEVs of right-handed sneutrinos, which ties the new
physics scale to the scale of the MSSM. We show here that this immediately
leads to an important prediction of two light sterile neutrinos, which can play
a significant role in the BBN and neutrino oscillations. We also discuss some
new relevant phenomenology for the LHC, in the context of the minimal
supersymmetric left-right symmetric theory which provides a natural setting for
the gauged $B-L$ symmetry.
