Trinification
In physics, the trinification model is a Grand Unified Theory proposed by Alvaro De Rújula, Howard Georgi and Sheldon Glashow in 1984.
Details
It states that the gauge group is eitheror
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, 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 as
and the gauge bosons as
Note that there are two Majorana neutrinos per generation. 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 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.
The trinification symmetry Lie algebra
is a maximal subalgebra of E6, whose matter representation 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.