Absolute minima and their stability in a new class of SO(10) models

Using a general method, we explicitly construct Higgs potentials in the new class of SO(10) models whose absolute minima correspond to the physically interesting symmetry-breaking patterns SO(10)→SU(2)/sub L/ x SU(2)/sub R/ x SU(4)C and SU(2)/sub L/ x SU(2)/sub R/ x SU(3)/sub C/ x U(1)/sub B//sub -//sub L/ x D. We show that there exist ranges of parameters in the Higgs potential of the 210 multiplet such that the SO(10) symmetry can be broken to SU(2)/sub L/ x SU(2)/sub R/ x SU(3)/sub C/ x U(1)/sub B//sub -//sub L/ directly or indirectly via SU(2)/sub L/ x SU(2)/sub R/ x SU(4)/sub C/ or SU(2)/sub L/ x SU(2)/sub R/ x SU(3)/sub C/ x U(1 )/sub B//sub -//sub L/ x D. In the supersymmetric version of the same model we find that the only left-right- symmetric breaking pattern consistent with unbroken super- symmetry is SU(2)/sub L/ x SU(2)/sub R/ x SU(3)/sub C/ x U(1 )/sub B//sub -//sub L/ x D