Trinification from E6 symmetry breaking

In the context of E-6 Grand Unified Theories (GUTs), an intriguing possibility for symmetry breaking to the Standard Model (SM) group involves an intermediate stage characterized by either SU(3) x SU(3) x SU(3) (trinification) or SU(6) x SU(2). The more common choices of SU(5) and SO(10) GUT symmetry groups do not offer such breaking chains. We argue that the presence of a real (rank 2 tensor) representation 650 of E-6 in the scalar sector is the minimal and likely only reasonable possibility to obtain one of the novel intermediate stages. We analyze the renormalizable scalar potential of a single copy of the 650 and find vacuum solutions that support regularly embedded subgroups SU(3) x SU(3) x SU(3), SU(6) x SU(2), and SO(10) x U(1), as well as specially embedded subgroups F-4 and SU(3) x G(2) that do not contain the SM gauge symmetry. We show that for a suitable choice of parameters, each of the regular cases can be obtained as the lowest among the analyzed minima in the potential.