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 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 $\mp=(8\pi G_N)^{-1/2}.$ Because of the large number of adjoint fields $\na$ coupled to S, one finds that M can be generically close to $\mgt=2\times 10^{16}\gev:$ $M\simeq \mp\exp[-16\pi^2 \log(3/2)/(\na+4)\lambda^2]$, 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.