Division algebraic symmetry breaking

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) $\mapsto$ Pati-Salam $\mapsto$ Left-Right symmetric $\mapsto$ 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($\mathbb{H}$). Upon the breaking of $su(2)_R$, our Higgs reduces to the familiar standard model Higgs.
Comment: Notation in this paper follows that of https://doi.org/10.1016/j.physletb.2022.136959 This article was first presented for Rutgers University, 2020. It was subsequently circulated widely amongst colleagues on the 16th of February, 2021. It was presented at the Perimeter Institute Conference on Octonions and the Standard model on the 15th of March, 2021. https://www.youtube.com/watch?v=4uTYBPRNX0s