Division algebraic symmetry breaking

TL;DR

This paper explores how division algebra structures induce a sequence of symmetry breakings in particle physics models, providing new insights into Higgs representations and symmetry transitions from octonions to the Standard Model.

Contribution

It introduces a novel framework linking division algebras to symmetry breaking sequences and explicitly demonstrates quaternionic triality's role in Higgs representations.

Findings

Identifies a symmetry breaking cascade from Spin(10) to the Standard Model.

Provides explicit quaternionic triality-based Higgs representations.

Connects division algebra structures to particle physics symmetry transitions.

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) $\mapsto$ 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.