Intermediate Symmetries in the Spontaneous Breaking of Supersymmetric SO

We study the supersymmetric spontaneous symmetry breaking of SO(10) into SU (3)⊗ SU (2) ⊗ U (1) for the most physically interesting cases of SU (5) or flipped SU (5) ⊗ U (1) intermediate symmetries. The first case is more easily realized while the second one requires a fine-tuning condition on the parameters of the superpotential. This is because in the case of SU (5) symmetry there is at most one singlet of the residual symmetry in each SO(10) irreducible representation. We also point out on more general grounds in supersymmetric GUT's that some intermediate symmetries can be exactly realized and others can only be approximated by fine-tuning. In the first category, there could occur some tunneling between the vacua with exact and approximate intermediate symmetry. The flipped SU (5)⊗U (1) symmetry improves the unification of gauge couplings if (B −L) is broken by (B − L) = 1 scalars yielding right handed neutrino masses below 10 14 GeV.