  We propose a mechanism for generating the GUT scale dynamically from the
Planck scale. The idea is that the GUT scale is fixed by the vacuum expectation
value of a "GUT modulus" field whose potential is exactly flat in the
supersymmetric limit. If supersymmetry is broken by gauge mediation, a
potential for the GUT modulus is generated at 2 loops, and slopes away from the
origin for a wide range of parameters. This potential is stabilized by
Planck-suppressed operators in the Kahler potential, and the GUT scale is fixed
to be of order M_* / (4\pi^2) (where M_* ~ 10^{18} GeV is the reduced Planck
scale) independently of the supersymmetry breaking scale. The cosmology of this
scenario is acceptable if there is an epoch of inflation with reheat
temperature small compared to the supersymmetry-breaking scale. We construct a
realistic GUT that realizes these ideas. The model is based on the gauge group
SU(6), and solves the doublet-triplet splitting problem by a sliding singlet
mechanism. The GUT sector contains no dimensionful couplings or tuned
parameters, and all mass scales other than the Planck scale are generated
dynamically. This model can be viewed as a realistic implementation of the
inverted hierarchy mechanism.
