Family Unification in Special Grand Unification

TL;DR

This paper explores a grand unified theory based on an $SU(19)$ gauge group in six dimensions, achieving family unification and anomaly cancellation without exotic fermions, using orbifold compactification.

Contribution

It introduces a novel $SU(19)$ GUT model on a 6D orbifold that unifies families and cancels anomalies without low-energy exotic fermions.

Findings

Three generations embedded in 6D bulk fermions.

Anomaly cancellation achieved with proper matter content.

No exotic chiral fermions at low energies.

Abstract

We discuss family unification in grand unified theory (GUT) based on an $SU(19)$ GUT gauge group broken to its subgroups including a special subgroup. In the $SU(19)$ GUT on the six-dimensional (6D) orbifold space $M^4\times T^2/\mathbb{Z}_2$, three generations of the 4D SM Weyl fermions can be embedded into a 6D bulk Weyl fermions in an $SU(19)$ second-rank anti-symmetric tensor representation. 6D and 4D gauge anomalies can be canceled out by considering proper matter content without 4D exotic chiral fermions at low energies.