In physics, the trinification model is a Grand Unified Theory proposed by Alvaro De Rújula, Howard Georgi and Sheldon Glashow in 1984.[1][2]


It states that the gauge group is either




and that the fermions form three families, each consisting of the representations:  ,  , and  . The L includes a hypothetical right-handed neutrino, which may account for observed neutrino masses (see neutrino oscillations), and a similar sterile "flavon."

There is also a   and maybe also a   scalar field called the Higgs field which acquires a vacuum expectation value. This results in a spontaneous symmetry breaking from

  to  .

The fermions branch (see restricted representation) as


and the gauge bosons as


Note that there are two Majorana neutrinos per generation (which is consistent with neutrino oscillations). Also, each generation has a pair of triplets   and  , and doublets   and  , which decouple at the GUT breaking scale due to the couplings




Note that calling representations things like   and (8,1,1) is purely a physicist's convention, not a mathematician's, where representations are either labelled by Young tableaux or Dynkin diagrams with numbers on their vertices, but it is standard among GUT theorists.

Since the homotopy group


this model predicts 't Hooft–Polyakov magnetic monopoles.

Trinification is a maximal subalgebra of E6, whose matter representation 27 has exactly the same representation and unifies the   fields. E6 adds 54 gauge bosons, 30 it shares with SO(10), the other 24 to complete its  .


  1. ^ De Rujula, A.; Georgi, H.; Glashow, S. L. (1984). "Trinification of all elementary particle forces". In Kang, K.; Fried, H.; Frampton, F. (eds.). Fifth Workshop on Grand Unification. Singapore: World Scientific.
  2. ^ Hetzel, Jamil; Stech, Berthold (2015-03-25). "Low-energy phenomenology of trinification: An effective left-right-symmetric model". Physical Review D. 91 (5): 055026. arXiv:1502.00919. doi:10.1103/PhysRevD.91.055026. ISSN 1550-7998.