ABSTRACT
This chapter focuses on a supersymmetric generalization of Einstein gravity — for a supergravity. Ordinary gravity is treated as the theory of a curved space–time. Any two coordinate systems are related by some Poincare transformation. It is the Poincare transformations which leave invariant the Minkowski metric. In the case of a curved space–time, there is no natural way to choose preferable coordinate systems; all coordinate systems are on the same footing. Conformal supergravity and Einstein supergravity, being gauge theories with the same gauge group, have different dynamical content. Conformal supergravity is described in terms of the gravitational superfield only, while Einstein supergravity needs one more dynamical superfield — the chiral compensator. The chapter discusses the component content of the supercurrent and the supertrace. It describes the technique of passing from superfields to component fields. The chapter presents a proper definition of the component fields of tensor superfields and discusses their transformation laws.
