Destabilizing Divergences in Supergravity Theories at Two Loops

We examine the stability of the mass hierarchy in hidden-sector supergravity theories. We show that a quadratically divergent tadpole can appear at two loops, even in minimal supergravity theories, provided the theory has a gauge- and global-symmetry singlet with renormalizable couplings to the visible fields. This tadpole can destabilize the hierarchy. We also find a quadratically divergent two-loop contribution to the field-dependent vacuum energy. This result casts doubt on the efficacy of the "LHC mechanism" for controlling quadratic divergences. We carry out the two-loop calculation in a manifestly supersymmetric formalism, and explain how to apply the formalism in the presence of supersymmetry breaking to derive radiative corrections to the supersymmetric and soft supersymmetry-breaking operators. Our approach greatly simplifies the calculation and guarantees consistency of our results with the underlying supergravity framework.