The Ultimate Trinification - American History Information Guide and Reference

In physics, the trinification model is a GUT theory.

It states that the gauge group is either

$SU(3)_C\times SU(3)_L\times SU(3)_R$

$[SU(3)_C\times SU(3)_L\times SU(3)_R]/\mathbb{Z}_3$ ;

and that the fermions form three families, each consisting of the representations : $(3,\bar{3},1)$ , $(\bar{3},1,3)$ and : $(1,3,\bar{3})$ .

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

There is also a $(1,3,\bar{3})$ and maybe also a $(1,\bar{3},3)$ scalar field called the Higgs field which acquires a VEV. This results in a spontaneous symmetry breaking from

$SU(3)_L\times SU(3)_R$ to $[SU(2)\times U(1)]/\mathbb{Z}_2$

and also,

$(3,\bar{3},1)\rightarrow(3,2)_{\frac{1}{6}}\oplus(3,1)_{-\frac{1}{3}}$ ,

$(\bar{3},1,3)\rightarrow2\,(\bar{3},1)_{\frac{1}{3}}\oplus(\bar{3},1)_{-\frac{2}{3}}$ ,

$(1,3,\bar{3})\rightarrow2\,(1,2)_{-\frac{1}{2}}\oplus(1,2)_{\frac{1}{2}}\oplus2\,(1,1)_0\oplus(1,1)_1$ ,

$(8,1,1)\rightarrow(8,1)_0$ ,

$(1,8,1)\rightarrow(1,3)_0\oplus(1,2)_{\frac{1}{2}}\oplus(1,2)_{-\frac{1}{2}}\oplus(1,1)_0$ ,

$(1,1,8)\rightarrow 4\,(1,1)_0\oplus 2\,(1,1)_1\oplus 2\,(1,1)_{-1}$ .

See restricted representation.

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

$(3,1)_{-\frac{1}{3}}$ and $(\bar{3},1)_{\frac{1}{3}}$

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

$(1,3,\bar{3})_H(3,\bar{3},1)(\bar{3},1,3)$

and

$(1,3,\bar{3})_H(1,3,\bar{3})(1,3,\bar{3})$ .

Note that calling the representations things like $(3,\bar{3},1)$ 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

$\pi_2\left(\frac{SU(3)\times SU(3)}{[SU(2)\times U(1)]/\mathbb{Z}_2}\right)=\mathbb{Z}$ ,

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

Categories: Particle physics

Your American History Reference Guide! - Trinification

Trinification

Your American History Reference Guide!
- Trinification