Chemistry - Flipped SU(5)

The Flipped SU(5) model is a GUT theory which states that the gauge group is [ SU(5) × U(1) ]/ $\mathbb{Z}_5$ and the fermions form three families, each consisting of the representations $\bar{5}_3$ , 10_-1 and 1_-5. This includes right-handed neutrinos, which are known to exist because of observed neutrino oscillations. There is also an adjoint scalar field, a 10_-1 and/or $\bar{10}_1$ called the Higgs field which acquires a VEV. This results in a spontaneous symmetry breaking from

$[SU(5)\times U(1)]/\mathbb{Z}_5$

$[SU(3)\times SU(2)\times U(1)]/\mathbb{Z}_6$

and also,

$\bar{5}_3\rightarrow (\bar{3},1)_{-\frac{2}{3}}\oplus (1,2)_{-\frac{1}{2}}$ , $10_{-1}\rightarrow (3,2)_{\frac{1}{6}}\oplus (\bar{3},1)_{\frac{1}{3}}\oplus (1,1)_0$ , $1_{-5}\rightarrow (1,1)_1$ , $24_0\rightarrow (8,1)_0\oplus (1,3)_0\oplus (1,1)_0\oplus (3,2)_{\frac{5}{6}}\oplus (\bar{3},2)_{-\frac{5}{6}}$ . See restricted representation.

Of course, calling the representations things like $\bar{5}_3$ and 24₀ 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

$\pi_2\left(\frac{[SU(5)\times U(1)]/\mathbb{Z}_5}{[SU(3)\times SU(2)\times U(1)]/\mathbb{Z}_6}\right)=0$

this model does not predicts monopoles. See Hooft-Polyakov monopole.

To do:

This theory was invented by ???.

Categories: Lie groups | Particle physics