Anomaly-Free Gauged R-Symmetry in Local Supersymmetry

We discuss local \R-symmetry as a potentially powerful new model building tool. We first review and clarify that a $U(1)$ \R-symmetry can only be gauged in local and not in global supersymmetry. We determine the anomaly-cancellation conditions for the gauged \R-symmetry. For the standard superpotential these equations have {\it no} solution, independently of how many Standard Model singlets are added to the model. There is also no solution when we increase the number of families and the number of pairs of Higgs doublets. When the Green-Schwarz mechanism is employed to cancel the anomalies, solutions only exist for a large number of singlets. We find many anomaly-free family-independent models with an extra $SU(3)_c$ octet chiral superfield. We consider in detail the conditions for an anomaly-free {\it family dependent} $ U(1)_R$ and find solutions with one, two, three and four extra singlets. Only with three and four extra singlets do we naturally obtain sfermion masses of order the weak-scale. For these solutions we consider the spontaneous breaking of supersymmetry and the $R$-symmetry in the context of local supersymmetry. In general the $U(1)_R$ gauge group is broken at or close to the Planck scale. We consider the effects of the \R-symmetry on baryon- and lepton-number violation in supersymmetry. There is no logical connection between a conserved \R-symmetry and conserved \R-parity. For conserved \R-symmetry we have models for all possibilities of conserved or broken \R-parity. Most models predict dominant effects which could be observed at HERA.