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We study several aspects of the quantum structure of the minimal potentiallyrealistic renormalizable $\mathrm{SO}(10)$ Higgs model in which the$\mathbf{45}\oplus \mathbf{126}$ scalars spontaneously break the symmetry downto the Standard Model group $\mathrm{SU}(3)_{c}\times \mathrm{SU}(2)_{L}\times\mathrm{U}(1)_{Y}$. With a complete information about the one-loop correctionsto the masses of all scalars in the theory and the one-loop beta functionsgoverning the running of all dimensionless scalar self-couplings, the domainsof the parameter space where the model can be treated perturbatively areestablished, along with improved bounds from the requirements of the SM vacuumstability and gauge coupling unification. We demonstrate that the model isfully consistent and potentially realistic only in very narrow regions of theparameter space corresponding to the breaking chains with well pronounced$\mathrm{SU}(4)_{C}\times \mathrm{SU}(2)_L\times \mathrm{U}(1)_R$ and$\mathrm{SU}(3)_{c}\times \mathrm{SU}(2)_L\times \mathrm{SU}(2)_R\times\mathrm{U}(1)_{B-L}$ intermediate symmetries, with a clear preference for theformer case. Barring accidental fine-tunings in the scalar sector, this makesit possible to provide a very sharp prediction for the position of theunification scale and the value of the associated gauge coupling, with clearimplications for the phenomenology of grand unified models based on thisstructure.

Quantum nature of the minimal potentially realistic $\mathrm{SO}(10)$ Higgs model