R-SYMMETRY BREAKING VERSUS SUPERSYMMETRY BREAKING

We point out a connection between R-symmetry and supersymmetry breaking. We show that the existence of an R-symmetry is a necessary condition for supersymmetry breaking and a spontaneously broken R-symmetry is a sufficient condition provided two conditions are satisfied. These conditions are: genericity, i.e. the effective lagrangian is a generic lagrangian consistent with the symmetries of the theory (no fine tuning), and calculability, i.e. the low-energy theory can be described by a supersymmetric Wess-Zumino effective lagrangian without gauge fields. All known models of dynamical supersymmetry breaking possess such a spontaneously broken R-symmetry and therefore contain a potentially troublesome axion. However, we use the fact that genericity is not a feature of supersymmetric theories, even when non-perturbative renormalization is included, to show that the R-symmetry can in many cases be explicitly broken without restoring supersymmetry and so the axion can be given an acceptably large mass.