331 models and grand unification: from minimal SU(5) to minimal SU(6)

We consider the possibility of grand unification of the SU(3)c⊗SU(3)L⊗U(1)X model in an SU(6) gauge unification group. Two possibilities arise. Unlike other conventional grand unified theories, in SU(6) one can embed the SU(3)c⊗SU(3)L⊗U(1)X model as a subgroup such that different multiplets appear with different multiplicities. Such a scenario may emerge from the flux breaking of the unified group in an E(6) F-theory GUT. This provides new ways of achieving gauge coupling unification in SU(3)c⊗SU(3)L⊗U(1)X models while providing the radiative origin of neutrino masses. Alternatively, a sequential variant of the SU(3)c⊗SU(3)L⊗U(1)X model can fit within a minimal SU(6) grand unification, which in turn can be a natural E(6) subgroup. This minimal SU(6) embedding does not require any bulk exotics to account for the chiral families while allowing for a TeV scale SU(3)c⊗SU(3)L⊗U(1)X model with seesaw-type neutrino masses