SU(6) (physics)
Encyclopedia
SU(6)
Special unitary group
The special unitary group of degree n, denoted SU, is the group of n×n unitary matrices with determinant 1. The group operation is that of matrix multiplication...

 is a grand unified theory which includes the Georgi-Glashow SU(5) gauge group.

The fermionic matter content of this model comes in three generations (copies) of


as SU(6) representations.

This gauge group is broken down to the Georgi-Glashow model by a pair of 6H/ Higgs fields.


The fermions decompose as


The Yukawa coupling causes 5 and a SU(5)-rep of fermions to pair up and acquire GUT scale masses for each generation.

An adjoint Higgs 35H breaks the model down further to the standard model
Standard Model
The Standard Model of particle physics is a theory concerning the electromagnetic, weak, and strong nuclear interactions, which mediate the dynamics of the known subatomic particles. Developed throughout the mid to late 20th century, the current formulation was finalized in the mid 1970s upon...

.

Most important, SU(6) is also used as a classification group for baryons and mesons. In fact it takes in account both SU(3) flavour and SU(2) spin. Then, quarks u,d,s, with spin up and down belong to the fundamental representation 6. Mesons belong to the 35 representation and baryons to the 56 representation obtained from the product quark-antiquark and quark-quark-quark, respectively.

Recently, a new type of grand unified theories based on SU(6) group has been proposed to realize a unification of strong and electroweak interactions . The work provides a complete form of 35 generators in SU(6) group.
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