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SU(6) 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

$15\oplus \overline{6}\oplus \overline{6}$

as SU(6) representations.

This gauge group is broken down to the Georgi-Glashow model by a pair of 6_H/${\overline{6}}_H$ Higgs fields.

$SU(6)\begin{array}{c}{6}_H/{\overline{6}}_H\\ ⟶\end{array}SU(5)\times U(1)$

The fermions decompose as

$15\to 10\oplus 5$

$\overline{6}\to \overline{5}\oplus 1$

The Yukawa coupling $\overline{6}{\overline{6}}_{H}15$ causes 5 and a $\overline{5}$ SU(5)-rep of fermions to pair up and acquire GUT scale masses for each generation.

An adjoint Higgs 35_H breaks the model down further to the standard model.

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.

References

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