Grand unification and proton stability based on a chiral SU(8) theory

We present a grand unified model of the strong, electromagnetic, and weak interactions based on a local $\mathrm{SU}{\mathrm{}\left(8\right)\mathrm{}}_L\times \mathrm{SU}{\mathrm{}\left(8\right)\mathrm{}}_R$ gauge theory which possesses a global $\mathrm{U}{\mathrm{}\left(8\right)\mathrm{}}_L\times \mathrm{U}{\mathrm{}\left(8\right)\mathrm{}}_R$ invariance. The model is spontaneously broken by the recently introduced neutrino-pairing mechanism, in which a Higgs field which transforms like a pair of right-handed neutrinos acquires a vacuum expectation value. This neutrino pairing breaks the model down to the standard Weinberg-Salam phenomenology. Further, the neutrino pairing causes the two initial global currents of the model, fermion number and axial fermion number, to mix with the non-Abelian local currents to leave unbroken two new global currents, namely, baryon number and a particular lepton number which counts charged leptons and left-handed neutrinos only. The exact conservations of these two resulting currents ensure the absolute stability of the proton, the masslessness of the observed left-handed neutrinos, and the standard lepton-number conservation of the usual weak interactions. A further feature of our model is the simultaneous absence of both strong $\mathrm{CP}$ violations and of observable axions. The model has a testable prediction, namely, the existence of an absolutely stable, relatively light, massive neutral lepton generated entirely from the right-handed-neutrino sector of the theory.