From Planck to GUT via dimensional transmutation

Consider a gauge singlet superfield S coupled to a pair of adjoint fields in a SUSY-GUT. If the tree-level vacuum is flat in S, the vev 〈S〉 which defines the GUT scale will be determined via dimensional transmutation at a scale M where the soft-breaking (mass)2 vanishes as a result of running from MP = (8πGN)−12. Because of the large number of adjoint fields NA coupled to S, one finds that M can be generically close to MGUT = 2 × 1016GeV: M≃Mp exp−16π2 log(32)(NA + 4)λ2, where λ is a Yukawa ∼ 0.7. This work examines the symmetries and dynamical constraints required in a SUSY-GUT in order that the desired flatness in S is achieved, and that this flatness may survive in a supergravity framework.