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${)}_L$×SU(2${)}_R$×SU(4)C and SU(2${)}_L$×SU(2${)}_R$×SU(3${)}_C$ ×U(1${)}_{B\mathrm{-}L}$×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${)}_L$×SU(2${)}_R$×SU(3${)}_C$ ×U(1${)}_{B\mathrm{-}L}$ directly or indirectly via SU(2${)}_L$×SU(2${)}_R$×SU(4${)}_C$ or SU(2${)}_L$×SU(2${)}_R$×SU(3${)}_C$×U(1${)}_{\mathrm{B}\mathrm{-}\mathrm{L}}$×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${)}_L$×SU(2${)}_R$×SU(3${)}_C$×U(1${)}_{\mathrm{B}\mathrm{-}\mathrm{L}}$×D.