Chapter 3: Curved superspace – Geometrical principles

This chapter is devoted to the introduction of an ad hoc curved superspace which extends the flat superspace of the previous chapter. In particular, the supergravity algebra, including local Lorentz transformations and superdiffeomorphims, will be defined. Dynamical superfields, i.e., supervierbein and spin superconnection will be introduced together with their associated curvature and tensor superfields. Since these superfields have too many degrees of freedom, some constraints upon the torsion tensors need to be imposed. The reduction of the Bianchi identities will enable us to express all curvature and torsion superfields in terms of three superfields only…