Supersymmetric Formulation of Gravity Theories with Nontrivial Lorentz Connection.

Using Breitenlohner's algebra, we have studied the supersymmetric extension of the 9-parameter gravity Lagrangian of Sezgin and van Nieuwenhuizen, which has the vierbein and the Lorentz connection as independent fields and no higher derivatives. The requirement that the theory be unitary and invariant under local supersymmetry transformations are so strict that the only feasible supersymmetric extension is ordinary Supergravity. The same holds for a more general 17-parameter Lagrangian considered by Neville. Our results seem to be deeply rooted in the structure of Breitenlohner's algebra. The linearized limit of it entails a decoupling of the Supergravity and the Lorentz connection sectors. Our results follow from the fact that the Lorentz connection belongs to a vector supermultiplet in the Wess-Zumino gauge.