Generation of grand unification hierarchies due to supergravity

We consider here the generation of stable hierarchies in an SO(10) grand unification scheme through supergravity: SO(10)→SU(2${)}_{\mathrm{L}}$×SU(2${)}_{\mathrm{R}}$×U(1${)}_{\mathrm{B}\mathrm{-}\mathrm{L}}$ ×SU(3${)}_{\mathrm{C}}$ (≡$G_{2213}$) in the zeroth order of supergravity, i.e., with global supersymmetry. The intermediate symmetry breaking $G_{2213}$→$G_{\mathrm{std}}$, and the Salam-Weinberg symmetry breaking $G_{\mathrm{std}}$→$G_{\mathrm{LE}}$ are then generated as the next two orders of corrections via supergravity. Supersymmetry is broken at the weak scale in the visible sector, which maintains the stability of the lower scales against the radiative corrections of the higher scales.