Stable hierarchies in O'Raifeartaigh models coupled to N=1 supergravity

A detailed analysis is made of a broad class of O'Raifeartaigh models coupled to N=1 supergravity with supersymmetry broken at an intermediate mass scale. These models may be considered either as an extension of the so-called "hidden sector" models, or as an extension of previously proposed globally supersymmetric models to include the effects of gravity. The effective low-energy potential is derived. The stability of the mass hierarchy in the absence of light singlets is demonstrated at the tree level and one-loop orders. Certain light scalars, however, can develop masses 10 TeV in some of these models.