Grand unification groups and charges of quarks and leptons

Abstract

The ansatz which demands that there exists a four-charge ($\frac{2}{3}$, $-\frac{1}{3}$, 0, -1) multiplet yields a strong restriction on the search for a grand unification group, $G=G_1\otimes G_2\otimes \cdots \otimes G_n\otimes \mathrm{U}\mathrm{}\left(1\right)\mathrm{}$. If the group is simple or semisimple, we have only two possibilities, $\mathrm{SU}\mathrm{}\left(n\right)\mathrm{}$ or $\mathrm{SU}\mathrm{}\left(n\right)\mathrm{}\otimes \mathrm{SU}\mathrm{}\left(m\right)\mathrm{}$.