Destabilizing Divergences in Supergravity Theories at Two Loops

TL;DR

The paper analyzes naturalness in hidden-sector supergravity by performing a manifestly supersymmetric two-loop calculation of quadratically divergent corrections. It shows that a gauge- and global-symmetry singlet with renormalizable visible-sector couplings can produce a quadratically divergent tadpole at two loops, destabilizing the mass hierarchy, and that a Yukawa-dependent quadratic divergence to the field-dependent vacuum energy also arises at two loops, undermining no-scale/LHC-type cancellations. Using a super-Weyl-Kähler invariant framework and compensator formalism, the authors map SUSY-breaking effects to radiative operators while preserving consistency with supergravity. The results indicate that one-loop cancellations do not persist at higher orders and that LHC models require additional, unlikely cancellations across multiple loops. The work provides a structured superspace method to identify dangerous divergences and assess their impact on the low-energy theory and soft SUSY-breaking terms.

Abstract

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.