Quaternionic and Octonionic Spinors. A Classification

TL;DR

This paper classifies quaternionic and octonionic spinors and Clifford algebras, providing explicit constructions, relations to G2 cosets, and applications to supersymmetry, superstrings, and M-theory extensions.

Contribution

It offers a comprehensive classification and explicit construction of quaternionic and octonionic spinors and Clifford algebras, including their applications in supersymmetry and M-theory.

Findings

Explicit recursive formulas for quaternionic and octonionic Clifford algebras

Systematic relations between octonionic Clifford algebras and G2 cosets

Applications to octonionic superstrings and M-superalgebra

Abstract

Quaternionic and octonionic realizations of Clifford algebras and spinors are classified and explicitly constructed in terms of recursive formulas. The most general free dynamics in arbitrary signature space-times for both quaternionic and octonionic spinors is presented. In the octonionic case we further provide a systematic list of results and tables expressing, e.g., the relations of the octonionic Clifford algebras with the $G_2$ cosets over the Lorentz algebras, the identities satisfied by the higher-rank antisymmetric octonionic tensors and so on. Applications of these results range from the classification of octonionic generalized supersymmetries, the construction of octonionic superstrings, as well as the investigations concerning the recently discovered octonionic $M$-superalgebra and its superconformal extension.