POSSIBLE NEW R-2 THEORY OF SUPERGRAVITY

We consider a new MacDowell-Mansouri R-2-type supergravity theory, an extension of conformal super gravity, based on the superalgebra Osp(1\ 8). Invariance under local symmetries with negative Weyl weight is ach ieved by imposing chirality-duality and double-duality constraints on curvatures, along with the usual constraint of vanishing supertorsion. An analysis of the remaining gauge symmetries shows that those with v anishing Weyl weight are invariances of the action at the linearized l evel. For the symmetries with positive Weyl weight we find that invari ance of the action would require further modifications of the transfor mation rules. This conclusion is supported by a kinematical analysis o f the closure of the gauge algebra.