Superalgebras of (split-)division algebras and the split octonionic M-theory in (6,5)-signature

TL;DR

This paper explores the use of (split-)division algebras, especially split-octonions, to construct generalized supersymmetries and M-algebras in various spacetime signatures, extending known octonionic M-theory frameworks.

Contribution

It introduces superalgebras based on (split-)division algebras and constructs a split-octonionic M-algebra in (6,5) signature, expanding the scope of octonionic M-theory.

Findings

Split-octonions enable a new M-algebra in (6,5) signature.

Reexpression of Clifford algebras using split-quaternions.

Extension of octonionic M-theory properties to different signatures.

Abstract

The connection of (split-)division algebras with Clifford algebras and supersymmetry is investigated. At first we introduce the class of superalgebras constructed from any given (split-)division algebra. We further specify which real Clifford algebras and real fundamental spinors can be reexpressed in terms of split-quaternions. Finally, we construct generalized supersymmetries admitting bosonic tensorial central charges in terms of (split-)division algebras. In particular we prove that split-octonions allow to introduce a split-octonionic M-algebra which extends to the (6,5) signature the properties of the 11-dimensional octonionic M-algebras (which only exist in the (10,1) Minkowskian and (2,9) signatures).