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 $M_{Pl} = (8 \pi G_N)^{-1/2}$. Because of the large number of adjoint fields $N_A$ coupled to S, one finds that M can be generically close to $M_{GUT} = 2 \times 10^{16} GeV$: $M \simeq M_{Pl} \exp[-16 \pi^2 \log(3/2) / (N_A+4) \lambda^2]$, where $\lambda$ is a Yukawa $\sim$ 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.