On the Octonionic M-algebra and Superconformal M-algebra

TL;DR

This paper introduces an octonionic variant of the M-algebra with fewer generators and interconnected sectors, and explores its superconformal extension, potentially linking to exceptional algebra structures in fundamental physics.

Contribution

It presents a novel octonionic formulation of the M-algebra with reduced generators and interconnected sectors, and constructs its superconformal version, highlighting unique algebraic features.

Findings

Octonionic M-algebra has 52 bosonic generators, fewer than the standard 528.

Octonionic M5 sector coincides with M1 and M2 sectors due to octonion non-associativity.

Superconformal octonionic M-algebra is given by OSp(1,8|O) with 239 bosonic and 64 fermionic generators.

Abstract

It is shown that the $M$-algebra related with the $M$ theory comes in two variants. Besides the standard $M$ algebra based on the real structure, an alternative octonionic formulation can be consistently introduced. This second variant has striking features. It involves only 52 real bosonic generators instead of 528 of the standard $M$ algebra and moreover presents a novel and surprising feature, its octonionic $M5$ (super-5-brane) sector is no longer independent, but coincides with the octonionic $M1$ and $M2$ sectors. This is in consequence of the non-associativity of the octonions. An octonionic version of the superconformal $M$-algebra also exists. It is given by $OSp(1,8|{\bf O})$ and admits 239 bosonic and 64 fermionic generators. It is speculated that the octonionic $M$-algebra can be related to the exceptional Lie and Jordan algebras that apparently play a special role in the Theory Of Everything.