Double SU(4) model

TL;DR

This paper explores a grand unified theory based on a Double SU(4) gauge group, unifying known particles and exotic states through symmetry breaking and group representations.

Contribution

It introduces the Double SU(4) model with detailed symmetry breaking, generator construction, and gauge boson matrices, extending the Gell-Mann Okubo relation.

Findings

Unified all known particles in multiplets of the gauge group

Derived gauge boson matrices and extended Gell-Mann Okubo relation

Outlined symmetry breaking pattern via Pati-Salam stage

Abstract

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.