In physics, the trinification model is a Grand Unified Theory proposed by Alvaro De Rújula, Howard Georgi and Sheldon Glashow in 1984.
It states that the gauge group is either
or
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
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
and
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 HooftâÂÂPolyakov magnetic monopoles.
The trinification symmetry Lie algebra is a maximal subalgebra of E<sub>6</sub>, whose matter representation has exactly the same representation and unifies the fields. E<sub>6</sub> adds 54 gauge bosons, 30 it shares with SO(10), the other 24 to complete its .