COULD THE SUPERSYMMETRIC HIGGS PARTICLES NATURALLY BE PSEUDO-GOLDSTONE BOSONS

The doublet-triplet splitting problem is perhaps the most problematic aspect of supersymmetric grand unified theories. It can be argued that the most natural reason for the Higgs doublets to be light is that th ey are pseudo-Goldstone bosons associated with the spontaneous breakdo wn of an accidental global symmetry. In this paper we discuss the poss ibility of implementing this idea in the SU(6) model of Refs. [11-14]. We show that although it is simple to generate an accidental symmetry of the renormalizable terms of the potential, it is quite difficult t o construct a model which allows for the preservation of the accidenta l symmetry in the nonrenormalizable terms. We summarize the constraint s on such models and then give three different ways to construct a sup erpotential where the dangerous mixing terms are sufficiently suppress ed even in the presence of nonrenormalizable operators. With these exa mples we demonstrate the existence of consistent models implementing t he Higgs as pseudo-Goldstone boson scheme. We extend one of the three examples to include fermion masses. We also show that when restricted to regular group embeddings the only possible models without light tri plets are trivial generalizations of the SU(6) model we consider.