On conformal superspace and the one-loop effective action in supergravity

We outline a program for the calculation of the one-loop effective action for generic supergravity theories in superspace. The first step involves the construction of a conformal superspace (with the conformal algebra as the structure group) to facilitate the algebraic manipulations necessary to deal with the underlying conformal coupling of chiral matter to supergravity. Next we show how to expand actions to second order in the fundamental quantum variables to allow one-loop computations. Finally, we describe how the chiral loops may be handled by explicitly calculating their divergences and anomalies.