  The Nelson-Seiberg theorem dictates conditions for the spontaneous breaking
of the supersymmetry in Wess-Zumino models with generic, possibly
non-renormalizable, superpotential; the existence of the R-symmetry is
necessary while the spontaneous breaking of the R-symmetry is sufficient. If we
restrict ourselves to generic but renormalizable theories, however, there exist
Wess-Zumino models whose vacua break the R-symmetry spontaneously while
preserving the supersymmetry. The classification and conditions of such
renormalizable exceptions are under active study. We give some new examples of
spontaneous breaking of the R-symmetry with preserved supersymmetry that are
not covered in the literature.
