The Theory of R-parity, Unification and SUSY at the LHC

Abstract. The simplest gauge theories for the conservation of R-parity in supersymmetry are discussed. We show how the minimal theory based on the B-L gauge symmetry predicts that R-parity must be spontaneously broken at the TeV scale. The most striking signals of these theories at the Large Hadron Collider are discussed. We present a realistic theory where the local baryon and lepton numbers are spontaneously broken at the supersymmetry breaking scale. The possibility to understand the conservation of R-parity in grand unified theories defined in four dimensions is mentioned