Radiative corrections in grand unified theories based on N=1 supergravity: nongauge theories

Abstract

Radiative corrections in grand unified theories (GUT's) based on N=1 supergravity are studied in the limit M_Planck→∞, with the gravitino mass m_g fixed, to all orders in perturbation theory. In this paper we study the effect of nongauge interactions only. It is shown that the tree-level mass hierarchy is not destroyed by the radiative corrections, provided there is no light field of mass «M_GUT, which transforms as a singlet under the subgroup that is unbroken at a scale above m_g. It is also pointed out that in the minimal supersymmetric SU(5) model, the addition of arbitrary soft-supersymmetry-breaking terms in the Lagrangian do not, in general, preserve the mass hierarchy, unless the coefficients of the soft-breaking terms are fine tuned. The fine tuning is automatic if the supersymmetry-breaking terms come from an underlying supergravity theory.