Flipped Su(5)

The Flipped SU(5) model is a GUT theory which states that the gauge group is href="/encyclopedia/Special-unitary-group" title="Special unitary group">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
U(1)/\mathbb{Z}_5
to
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{U(1)/\mathbb{Z}_5}{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 ???.

 

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