On destabilizing divergences in supergravity models

We show that, for standard N = 1 supergravity coupled to chiral matter, if the Kähler potential has no terms linear in chiral superfields, then none are generated through quadratically divergent one-loop corrections. This holds whether or not the Kähler potential contains terms cubic in chiral (and antichiral) matter superfields. If however the cosmological constant vanishes and SUSY is spontaneously broken, linear terms are present and new quadratically divergent linear terms may be generated due to the presence of nonvanishing Kähler curvature. These can potentially destabilize the weak-scale hierarchy. We discuss the importance of this for effective supergravity models which contain standard model singlets.