Implications of a dark grand unification

Abstract: Given that dark matter and normal matter are nontrivially unified in a grand unified theory, called dark grand unification, we derive novel residual theories at low energy explaining dark matter and neutrino mass. The first chain of which is $E_6\to SU(3)_C\otimes SU(3)_L\otimes SU(3)_R$, which contains a matter parity by itself stabilizing a dark matter candidate and producing neutrino mass via a seesaw. The second chain is $\mathrm{Trinification}\to SU(3)_C \otimes SU(3)_L\otimes U(1)_X\otimes U(1)_N$, which results in a novel family-universal 3-3-1-1 model, opposite to the normal 3-3-1-1 (or corresponding 3-3-1) model. Surprisingly, it is a variant of both minimal 3-3-1 model and 3-3-1 model with right-handed neutrinos since both $e_R$ and $\nu_R$ are located at the bottoms of lepton triplets. Since this universal 3-3-1-1 model is properly embedded in the trinification, the above matter parity works governing dark matter stability as well as suppressing unwanted fermion mixings. Further, neutrino masses are naturally generated by a canonical seesaw too.