CP violation from flavor symmetry in a lepton quarticity dark matter model

We propose a simple Δ(27)⊗Z4 model where neutrinos are predicted to be Dirac fermions. The smallness of their masses follows from a type-I seesaw mechanism and the leptonic CP violating phase correlates with the pattern of Δ(27) flavor symmetry breaking. The scheme naturally harbors a WIMP dark matter candidate associated to the Dirac nature of neutrinos, in that the same Z4 lepton number symmetry also ensures dark matter stability.