Family Unification in $SO(16)$ Grand Unification

TL;DR

This paper presents a 6D $SO(16)$ grand unified model unifying SM gauge groups and family symmetry, with anomaly cancellation and a weakening gauge coupling at high energies.

Contribution

It introduces a novel 6D $SO(16)$ GUT model unifying SM and family symmetries with anomaly cancellation mechanisms.

Findings

6D $SO(16)$ gauge anomaly canceled by vectorlike fermions.

4D gauge anomalies canceled by localized fermions at fixed points.

The $SO(16)$ gauge coupling becomes weaker at high energies.

Abstract

We propose a unified model for the three Standard Model (SM) gauge symmetries and $SU(3)$ family symmetry based on $SO(16)$ grand unified gauge symmetry on six-dimensional (6D) spacetime. In this model, three chiral generations of quarks and leptons are unified into a 6D Weyl fermion in the spinor representation of $SO(16)$. The 6D $SO(16)$ gauge anomaly is canceled by the vectorlike nature of the model, and the 4D gauge anomalies are canceled by introducing suitable 4D localized fermions at the fixed point. The 4D gauge coupling constant of $SO(16)$ has the property of becoming weaker at high energies.