NATURAL GAUGE HIERARCHY IN SO(10)

It is shown that a natural gauge hierarchy and doublet-triplet splitting can be achieved in SO(10) using the Dimopoulos-Wilczek mechanism. Artificial cancellations (fine-tuning) and arbitrary forms of the superpotential are avoided, the superpotential being the most generally compatible with a symmetry. It is shown by example that the Dimopoulos-Wilczek mechanism can be protected against the effects of higher-dimension operators possibly induced by Planck-scale physics. Natural implementation of the mechanism leads to an automatic Peccei-Quinn symmetry. The same local symmetries that would protect the gauge hierarchy against Planck-scale effects tend to protect the axion also. How realistic quark and lepton masses might arise in this framework is discussed. It is shown how the theory may remain perturbative up to the Planck scale. It is also argued that ''weak suppression'' of proton decay can be implemented more economically than can ''strong suppression,'' offering some grounds to hope [in the context of SO(10)] that proton decay could be seen at SuperKamiokande.