Grand unification and the Planck scale: an SO(10) example of radiative symmetry breaking

Grand unification of gauge couplings and fermionic representations remains an appealing proposal to explain the seemingly coincidental structure of the Standard Model. However, to realise the Standard Model at low energies, the unified symmetry group has to be partially broken by a suitable scalar potential in just the right way. The scalar potential contains several couplings, whose values dictate the residual symmetry at a global minimum. Some (and possibly many) of the corresponding symmetry-breaking patterns are incompatible with the Standard Model and therefore non-admissible.