- Trinification
In
physics , the trinification model is a GUT theory.It states that the
gauge group is either:SU(3)_C imes SU(3)_L imes SU(3)_R
or
:SU(3)_C imes SU(3)_L imes SU(3)_R] /mathbb{Z}_3;
and that the fermions form three families, each consisting of the representations :3,ar{3},1), ar{3},1,3) and :1,3,ar{3}).
This includes the right-handed neutrino, which can account for observed neutrino masses (but has not yet been proved to exist). See
neutrino oscillation s.There is also a 1,3,ar{3}) and maybe also a 1,ar{3},3)
scalar field called theHiggs field which acquires a VEV. This results in aspontaneous symmetry breaking from:SU(3)_L imes SU(3)_R to SU(2) imes U(1)] /mathbb{Z}_2
and also,
:3,ar{3},1) ightarrow(3,2)_{frac{1}{6oplus(3,1)_{-frac{1}{3,
:ar{3},1,3) ightarrow2,(ar{3},1)_{frac{1}{3oplus(ar{3},1)_{-frac{2}{3,
:1,3,ar{3}) ightarrow2,(1,2)_{-frac{1}{2oplus(1,2)_{frac{1}{2oplus2,(1,1)_0oplus(1,1)_1,
:8,1,1) ightarrow(8,1)_0,
:1,8,1) ightarrow(1,3)_0oplus(1,2)_{frac{1}{2oplus(1,2)_{-frac{1}{2oplus(1,1)_0,
:1,1,8) ightarrow 4,(1,1)_0oplus 2,(1,1)_1oplus 2,(1,1)_{-1}.
See
restricted representation .Note that there are two Majorana neutrinos per generation (which is consistent with
neutrino oscillation s). Also, a copy of3,1)_{-frac{1}{3 and ar{3},1)_{frac{1}{3
as well as
1,2)_{frac{1}{2 and 1,2)_{-frac{1}{2
per generation decouple at the GUT breaking scale due to the couplings
1,3,ar{3})_H(3,ar{3},1)(ar{3},1,3)
and
1,3,ar{3})_H(1,3,ar{3})(1,3,ar{3}).
Note that calling the representations things like 3,ar{3},1) and (8,1,1) is purely a physicist's convention, not a mathematician's convention, where representations are either labelled by
Young tableau x orDynkin diagram s with numbers on their vertices, but still, it is standard among GUT theorists.Since the
homotopy group pi_2left(frac{SU(3) imes SU(3)}{ [SU(2) imes U(1)] /mathbb{Z}_2} ight)=mathbb{Z},
this model predicts
monopoles . See't Hooft-Polyakov monopole .This model is suggested by
Sheldon Lee Glashow ,Howard Georgi andAlvaro de Rujula , in 1984. This is one of themaximal subalgebra of E6, whose matter representation 27 has exactly the same representation as above.
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