Supersymmetric formulation of gravity theories with nontrivial Lorentz connection.

Abstract

Using Breitenlohner's algebra, we study the supersymmetric extension of the 9-parameter gravity Lagrangian of Sezgin and van Nieuwenhuizen, which has the vierbein and Lorentz connection as independent fields. The requirements 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. We discuss the close relationship between our results and the structure of the supersymmetry transformations of Breitenlohner's potentials.