The Origin of Families and $SO(18)$ Grand Unification

TL;DR

This paper proposes a novel approach to the family puzzle in particle physics using topological superconductor insights within SO(18) grand unification, suggesting new symmetry breaking patterns that yield three light families.

Contribution

It introduces a new symmetry breaking scheme in SO(18) GUTs that naturally results in three light families, integrating condensed matter theory concepts.

Findings

A pattern of symmetry breaking leads to three light families.

Yukawa couplings of intermediate strength decouple mirror matter.

Incorporates topological superconductor advances into particle physics models.

Abstract

We exploit a recent advance in the study of topological superconductors to propose a solution to the family puzzle of particle physics in the context of SO(18) (or more correctly, Spin(18)) grand unification. We argue that Yukawa couplings of intermediate strength may allow the mirror matter and extra families to decouple at arbitrarily high energies. As was clear from the existing literature, we have to go beyond the Higgs mechanism in order to solve the family puzzle. A pattern of symmetry breaking which results in the SU(5) grand unified theory with horizontal or family symmetry USp(4) = Spin(5) (or more loosely, SO(5)) leaves exactly three light families of matter and seems particularly appealing. We comment briefly on an alternative scheme involving discrete non-abelian family symmetries. In a few lengthy appendices we review some of the pertinent condensed matter theory.