Octonions and M-theory

TL;DR

This paper explores the fundamental role of octonions and related exceptional structures in M-theory, highlighting their appearance in compactification spaces, symmetry groups, and brane configurations, and emphasizing the need for deeper understanding of octonionic properties.

Contribution

It provides a comprehensive review of how octonionic structures underpin various aspects of M-theory, connecting algebraic and geometric entities in a unified framework.

Findings

Exceptional Lie groups appear in M-theory.

G_2-holonomy manifolds relate to M2 branes and 3-form.

Octonions' non-associativity is crucial for future insights.

Abstract

We explain how structures related to octonions are ubiquitous in M-theory. All the exceptional Lie groups, and the projective Cayley line and plane appear in M-theory. Exceptional G_2-holonomy manifolds show up as compactifying spaces, and are related to the M2 Brane and 3-form. We review this evidence, which comes from the initial 11-dim structures. Relations between these objects are stressed, when extant and understood. We argue for the necessity of a better understanding of the role of the octonions themselves (in particular non-associativity) in M-theory.