Editing Grand Unified Theory (section)

=== Extended Grand Unified Theories ===
Non-chiral extensions of the Standard Model with vectorlike split-multiplet particle spectra which naturally appear in the higher SU(N) GUTs considerably modify the desert physics and lead to the realistic (string-scale) grand unification for conventional three quark-lepton families even without using [[supersymmetry]] (see below). On the other hand, due to a new missing VEV mechanism emerging in the supersymmetric SU(8) GUT the simultaneous solution to the gauge hierarchy (doublet-triplet splitting) problem and problem of unification of flavor can be argued.<ref>J.L.Chkareuli, SU(N) SUSY GUTS WITH STRING REMNANTS: MINIMAL SU(5) AND BEYOND, Invited Talk given at 29th International Conference on High-Energy Physics (ICHEP 98), Vancouver, 23–29 July 1998. In *Vancouver 1998, High energy physics, vol. 2 1669–73</ref>

'''GUTs with four families / generations, SU(8)''': Assuming 4 generations of fermions instead of 3 makes a total of {{math|'''64'''}} types of particles. These can be put into {{math|'''64''' {{=}} '''8''' + '''56'''}} representations of {{math|SU(8)}}. This can be divided into {{math|SU(5) × SU(3)<sub>F</sub> × U(1)}} which is the {{math|SU(5)}} theory together with some heavy bosons which act on the generation number.

'''GUTs with four families / generations, O(16)''': Again assuming 4 generations of fermions, the '''128''' particles and anti-particles can be put into a single spinor representation of {{math|O(16)}}.