Double SU(4) model

In this manuscript we study the Double SU(4) model as a grand unified theory based on the gauge group $,SU(4)\times SU(4)\left(\times $\mathcal{Z}$_2\right)$. A complete set of generators is constructed according to a pattern of symmetry breaking via a Pati-Salam stage. Furthermore, the gauge boson matrices are derived and the extended Gell-Mann Okubo relation is calculated. All known elementary particles and antiparticles, besides exotic degrees of freedom, are unified in multiplets which are transformed as $(4,4)$ and $(\bar{4},\bar{4})$ under the proposed gauge group.