Consistency problems of hypergravity

The constraints arising upon coupling a massless spin 5/2 field to gravity are analyzed. In contrast to supergravity, they depend not only on the Einstein tensor, but also on the off-shell (Weyl) components of the curvature. The latter contributions do vanish, however, for 'self-dual' systems, i.e., half-flat gravitational and pure (left/right) helicity spin 5/2 fields. (Auth.)