SUPERSPACE BIANCHI IDENTITIES AND THE SUPER-COVARIANT DERIVATIVE

We analyze the theory of supergravity, with minimal component fields, in spacetimes of two, three, and four dimensions. The analyses begins by investigating the superspace Bianchi identities. We show that in two and three dimensions, the supergravity multiplet consists of the gravition, gravitino, and a single auxiliary field. In four dimensions, we analyze the Bianchi identities in order to investigate the structure of the veilbein and connection superfields. Utilizing this analysis, we explicitly construct these superfields to quadratic order in θ and give a prescription for determining them completely. © 1979.