On a vector superfield generated by the supercurrent

Abstract

The supercurrent of Ferrara and Zumino is a vector superfield including the energy-momentum tensor and the spin-vector supersymmetry current. The Einstein equations can be viewed as equations for a tensor field with the energy-momentum tensor as a source. By analogy one can hope that the simplest supersymmetric version of the gravitational theory is the theory of a vector superfield with the supercurrent as a source. We consider (in the lowest order) the interaction of the vector superfield with matter chiral and general scalar superfields. The scalar chiral superfield transformations obtained form a closed algebra including gravitational and local supersymmetry transformations. This construction can be a first step to a superfield formulation of supergravity.