Octions: An E8 description of the Standard Model

Abstract

We interpret the elements of the exceptional Lie algebra [Formula: see text] as objects in the Standard Model, including lepton and quark spinors with the usual properties, the Standard Model Lie algebra [Formula: see text], and the Lorentz Lie algebra [Formula: see text]. Our construction relies on identifying a complex structure on spinors and then working in the enveloping algebra. The resulting model naturally contains Grand Unified Theories based on SO(10) (Georgi), SU(5) (Georgi–Glashow), and SU(4) ×SU(2) ×SU(2) (Pati–Salam). We then briefly speculate on the role of the remaining elements of [Formula: see text] and propose a mechanism leading to exactly three generations of particles.