Supercurrents in N=1 Minimal Supergravity in the Superconformal Formalism

We discuss the Einstein tensor, the supercurrent and their conservation laws of old and new minimal formulations of supergravity in the superconformal approach. The variation of the action with respect to the gauge field of the $R$-symmetry in the conformal approach (the auxiliary field in the super-Poincaré action) allows to find the Einstein tensor and supercurrent in any curved background. Hence generalized expressions for their Ward identities follow. This proceeding is based on [1, 2].