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We consider the possibility of grand unification of the $\mathrm{ SU(3)_c\otimes SU(3)_L \otimes U(1)_X}$ model in an SU(6) gauge unification group. Twopossibilities arise. Unlike other conventional grand unified theories, in SU(6)one can embed the $\mathrm{ SU(3)_c \otimes SU(3)_L \otimes U(1)_X}$ model as asubgroup such that different multiplets appear with different multiplicities.Such a scenario may emerge from the flux breaking of the unified group in anE(6) F-theory GUT. This provides new ways of achieving gauge couplingunification in $\mathrm{ SU(3)_c \otimes SU(3)_L \otimes U(1)_X}$ models whileproviding the radiative origin of neutrino masses. Alternatively, a sequentialvariant of the $\mathrm{ SU(3)_c \otimes SU(3)_L \otimes U(1)_X}$ model can fitwithin 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 toaccount for the chiral families while allowing for a TeV scale $\mathrm{SU(3)_c \otimes SU(3)_L \otimes U(1)_X}$ model with seesaw-type neutrinomasses.

331 Models and Grand Unification: From Minimal SU(5) to Minimal SU(6)