Fermion-sector frustrated SU(4) as a preonic precursor of the standard model

We give a model for composite quarks and leptons based on the semisimple gauge group SU(4), with the preens in the 10 representation; this choice of gauge gluon and preen multiplets is motivated by the possibility of embedding them in an N = 6 supergravity multiplet, with the preens and antipreons both in the 20 of SU(6). Hypercolor singlets are forbidden in the fermionic sector of this theory; we propose that the SU(4) symmetry spontaneously breaks to SU(3) x U(1), with the binding of triality nonzero preens and gluons into composites, and with the formation of a color singlet condensate that breaks the initial Z(12) vacuum symmetry to Z(6). The spin 1/2 fermionic composites have the triality structure of a quark-lepton family, and the initial Z(12) symmetry implies that there are six massless families, which mix to give three distinct families below the scale of the condensate. The spin 1 triality aero composites of the color triplet SU(4) gluons, when coupled to the condensate and with the color singlet representation of the 10 acting as a doorway state, lead to weak interactions of the fermionic composites through an SU(2) gauge algebra. The initial Z(12) symmetry implies that this SU(2) gauge algebra structure is doubled, which in turn permits the corresponding independent gauge bosons to couple to chiral components of the composite fermions. Since the U(1) couples to the 10 representation as B - L, an effective SU(2)(L) x SU(2)(R) x U(1)(B-L) electroweak theory arises at the condensate scale, with all composites having the correct electric charge structure. Assuming a mechanism for forming composite Higgs bosons, the Z(12) --> Z(6) symmetry breaking chain implies that below the condensate scale there can be two sets of discrete chiral Z(6) triplets of Higgs doublets, as required by a phenomenological model for the CKM matrix that we have analyzed in detail elsewhere. A renormalization group analysis of the SU(4) model shows that the conversion by binding of one 10 of SU(4) to 12 triplets of SU(3) can give a very large, calculable hierarchy ratio between the SU(4) and the hadronic mass scales.