Supernova Bounds on Supersymmetric $R$-parity Violating Interactions

We re-examine resonant massless-neutrino conversions in a dense medium induced by flavour changing neutral current (FCNC) interactions. We show how the observed $\bar\nu_e$ energy spectra from SN1987a and the supernova $r$-process nucleosynthesis provide constraints on supersymmetric models with $R$ parity violation, which are much more stringent than those obtained from the laboratory. We also suggest that resonant massless-neutrino conversions may play a positive role in supernova shock reheating. Finally, we examine the constraints on explicit $R$-parity-violating FCNCs in the presence of non-zero neutrino masses in the eV range, as indicated by present hot dark matter observations.