Se p 19 93 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 cal-culability, 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 nonperturbative renormalization is included, to show that the R symmetry can in many cases be explicitly broken without restoring supersym-metry and so the axion can be given an acceptably large mass.