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

TL;DR

In $Spin(18)$ grand unification, all fermions live in a single $256^+$ spinor, but a mirror $256^-$ sector complicates the low-energy spectrum. The authors leverage the Kitaev-Wen mechanism from condensed matter physics to generate a mass gap for fermions without explicit mass terms, keeping gauge bosons massless and allowing decoupling of mirror and extra families under carefully chosen Yukawa couplings and scalar masses. They analyze two breaking routes, $Spin(18) o Spin(10) imes Spin(8)$ and $Spin(18) o U(9)$, showing how mirror sector decoupling and three light Standard Model families can emerge, with a path to a horizontal symmetry such as $SU(5) imes USp(4)$ that yields exactly three families. They also discuss alternative flavor constructions via non-abelian discrete groups and outline the key open issue of realizing the required Yukawa conditions in explicit models, along with potential phenomenological implications if the extra states are accessible at colliders.

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.