Gravitational radiative corrections in N=1 supergravity.

Abstract

In an ungauged $N=1$ supergravity theory defined on an arbitrary Kahlerian manifold we compute the divergent one-loop corrections to the bosonic part of the effective action. Although the theory is not renormalizable such a calculation may be of relevance in view of the fact that $N=1$ supergravities emerge as effective nonrenormalizable theories in the low-energy limit of some superstring models. In our calculations we have committed ourselves neither to a particular four-dimensional geometry nor to a particular Kahlerian manifold. We pay special attention to the one-loop scalar potential of the theory. We show that, by a proper redefinition of the metric, geometric objects such as scalar curvature can be made not to interact with the scalars and the definition of the potential of the theory becomes in this way unambiguous.