$SU(3) \times SO(10)$ in 6d

TL;DR

This paper presents a 6-dimensional $SU(3) imes SO(10)$ unified gauge theory with orbifold compactification that naturally explains fermion families, their masses, mixings, and CP phases, while controlling proton decay and enabling leptogenesis.

Contribution

It introduces a simple 6d orbifold model with specific boundary conditions that generate realistic fermion mass hierarchies and mixing patterns without extra driving or messenger fields.

Findings

Successfully reproduces neutrino mixing alignments.

Provides a natural explanation for three fermion families.

Ensures proton stability and supports leptogenesis.

Abstract

We discuss a simple and elegant $SU(3)\times SO(10)$ family unified gauge theory in 6d compactified on a torus with the orbifold $T_2/Z_2^3$ and supplemented by a $Z_6\times Z_3$ discrete symmetry. The orbifold boundary conditions generate all the desired $SU(3)$ breaking vacuum alignments, including the $(0,1,-1)$ and $(1,3,-1)$ alignments of the Littlest Seesaw model for atmospheric and solar neutrino mixing, as well as the usual $SO(10)$ breaking with doublet-triplet splitting. The absence of driving and messenger fields considerably simplifies the field content of the model. It naturally explains why there are three families of quarks and leptons, and accounts for all their masses, mixing angles and CP phases via rather elegant looking Yukawa and Majorana matrices in the theory basis. The resulting model controls proton decay and allows successful Leptogenesis.