String completion of an SU(3)c ⊗ SU(3)L ⊗ U(1)X electroweak model

The extended electroweak SU(3)c⊗SU(3)L⊗U(1)XSU(3)c⊗SU(3)L⊗U(1)X symmetry framework “explaining” the number of fermion families is revisited. While 331-based schemes can not easily be unified within the conventional field theory sense, we show how to do it within an approach based on D-branes and (un)oriented open strings, on Calabi–Yau singularities. We show how the theory can be UV-completed in a quiver setup, free of gauge and string anomalies. Lepton and baryon numbers are perturbatively conserved, so neutrinos are Dirac-type, and their lightness results from a novel TeV scale seesaw mechanism. Dynamical violation of baryon number by exotic instantons could induce neutron–antineutron oscillations, with proton decay and other dangerous R-parity violating processes strictly forbidden.