Flipped SU(5)
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The Flipped SU(5) model is a GUT theory which states that the gauge group is [ SU(5) × U(1) ]/<math>\mathbb{Z}_5<math> and the fermions form three families, each consisting of the representations <math>\bar{5}_3<math>, 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 <math>\bar{10}_1<math> called the Higgs field which acquires a VEV. This results in a spontaneous symmetry breaking from
- <math>[SU(5)\times U(1)]/\mathbb{Z}_5<math>
to
- <math>[SU(3)\times SU(2)\times U(1)]/\mathbb{Z}_6<math>
and also,
- <math>\bar{5}_3\rightarrow (\bar{3},1)_{-\frac{2}{3}}\oplus (1,2)_{-\frac{1}{2}}<math>, <math>10_{-1}\rightarrow (3,2)_{\frac{1}{6}}\oplus (\bar{3},1)_{\frac{1}{3}}\oplus (1,1)_0<math>, <math>1_{-5}\rightarrow (1,1)_1<math>, <math>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}}<math>. See restricted representation.
Of course, calling the representations things like <math>\bar{5}_3<math> 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
- <math>\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<math>
this model does not predicts monopoles. See Hooft-Polyakov monopole.
To do:
- This theory was invented by ???.