Division algebraic symmetry breaking

Abstract

Reframing certain well-known particle models in terms of normed division algebras leads to two new results for BSM physics.(1) We identify a sequence of complex structures which induces a cascade of breaking symmetries: Spin(10) ↦ Pati-Salam ↦ Left-Right symmetric ↦ Standard model + B-L (both pre- and post-Higgs-mechanism). These complex structures derive from the octonions, then from the quaternions, then from the complex numbers.(2) We provide, also for the first time we believe, an explicit demonstration of left-right symmetric Higgs representations stemming from quaternionic triality, tri(H). Upon the breaking of su(2)R, our Higgs reduces to the familiar standard model Higgs.