When reading about GUTs you often come across the 'Standard Model decomposition' of the representations of a given gauge group. ie. you get the Standard Model gauge quantum numbers arranged between some brackets. For example, here are a few SM decompositions of the SU(5) representations [itex]\textbf{5}, \textbf{10}, \textbf{15}[/itex] and [itex]\textbf{24}[/itex].(adsbygoogle = window.adsbygoogle || []).push({});

So, for instance this is telling us that the representation [itex]\textbf{5}[/itex] will contain fields that are either

([itex]SU(3)_{C}[/itex] triplet, [itex]SU(2)_{L}[/itex] singlet, hypercharge [itex]\tfrac{1}{2}Y = -\tfrac{1}{3}[/itex]) for the (3, 1, [itex]-\tfrac{1}{3}[/itex]),

or

([itex]SU(3)_{C}[/itex] singlet, [itex]SU(2)_{L}[/itex] doublet, hypercharge [itex]\tfrac{1}{2}Y = \tfrac{1}{2}[/itex]) for the (1, 2, [itex]\tfrac{1}{2}[/itex]).

That's straightforward enough. However, I can't seem to find anything online explaining how these have been determined. I can find plenty about how you might go about constructing the [itex]\textbf{10}, \textbf{15}[/itex] and [itex]\textbf{24}[/itex] starting from combinations of the fundamental [itex]\textbf{5}[/itex] by the 'Young's Tableaux' method, but nothing about starting with one of these SU(5) representations and breaking them down. Can anyone explain or link to an explanation?

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Standard Model decompositions of larger group representations?

Loading...

Similar Threads - Standard Model decompositions | Date |
---|---|

A Conformal window | Jan 22, 2018 |

I Standard Model (Forces interacting with Matter) | Jan 8, 2018 |

A A symmetric model for leptons | Jan 2, 2018 |

A My T-shirt and the Standard Model | Dec 11, 2017 |

A SU(5), 'Standard Model decomposition', direct sum etc. | Jul 29, 2016 |

**Physics Forums - The Fusion of Science and Community**