From Planck to GUT via Dimensional Transmutation

Abstract

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.

13 pages, 1 figure, uses Latex and epsf, reference added

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