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

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.

31 pages, no figures. v2: minor changes, added subsection II.3

References in corpus (7)

• Classification of topological insulators and superconductors in three spatial dimensions
• Physics of three dimensional bosonic topological insulators: Surface Deconfined Criticality and Quantized Magnetoelectric Effect
• Symmetry Protected Topological States of Interacting Fermions and Bosons
• Neutrino mixing from the double tetrahedral group T^{\prime}
• Massive fermions without fermion bilinear condensates
• Interacting Topological Insulator and Emergent Grand Unified Theory
• Fermion mass without symmetry breaking

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