In physics, the trinification model is a GUT theory.

It states that the gauge group is either

or

;

and that the fermions form three families, each consisting of the representations :, and :.

This includes the right-handed neutrino, which is now known to exist. See neutrino oscillations.

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

to

and also,

,

,

,

,

,

.

See restricted representation.

Note that there are two Majorana neutrinos per generation (which is consistent with neutrino oscillations). Also, a copy of

and

as well as

and

per generation decouple at the GUT breaking scale due to the couplings

and

.

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

Since the homotopy group

,

this model predicts monopoles. See 't Hooft-Polyakov monopole.