DESTABILIZING DIVERGENCES IN SUPERGRAVITY THEORIES AT 2 LOOPS

We examine the stability of the mass hierarchy in hidden-sector supegr avity theories. We show that a quadratically divergent tadpole can app ear at two loops, even in minimal supergravity theories, provided the theory has a gauge- and global-symmetry singlet with renormalizable co uplings to the visible fields. This tadpole can destabilize the hierar chy. We also find a quadratically divergent two-loop contribution to t he field-dependent Vacuum energy. This result casts doubt on the effic acy of the ''LHC mechanism'' for controlling quadratic divergences. We carry out the two-loop calculation in a manifestly supersymmetric for malism, and explain how to apply the formalism in the presence of supe rsymmetry breaking to derive radiative corrections to the supersymmetr ic and soft supersymmetry-breaking operators. Our approach greatly sim plifies the calculation and guarantees consistency of our results with the underlying supergravity framework.