Octonionic M-theory and D=11 generalized conformal and superconformal algebras

TL;DR

This paper explores the application of octonionic structures to D=11 M-theory, deriving new superalgebras and conformal algebras with extended bosonic and fermionic charges using octonionic matrices.

Contribution

It introduces octonionic formulations of D=11 superalgebras and conformal algebras, revealing new algebraic structures and charge configurations in M-theory.

Findings

Derived octonionic D=11 superalgebra with 52 bosonic charges

Constructed octonionic D=11 conformal algebra with 232 bosonic charges

Extended to octonionic superconformal algebra with 64 fermionic and 239 bosonic generators

Abstract

Following [1] we further apply the octonionic structure to supersymmetric D=11 $M$-theory. We consider the octonionic $2^{n+1} \times 2^{n+1}$ Dirac matrices describing the sequence of Clifford algebras with signatures ($9+n,n$) ($n=0,1,2, ...$) and derive the identities following from the octonionic multiplication table. The case $n=1$ ($4\times 4$ octonion-valued matrices) is used for the description of the D=11 octonionic $M$ superalgebra with 52 real bosonic charges; the $n=2$ case ($8 \times 8$ octonion-valued matrices) for the D=11 conformal $M$ algebra with 232 real bosonic charges. The octonionic structure is described explicitly for $n=1$ by the relations between the 528 Abelian O(10,1) tensorial charges $Z_\mu Z_{\mu\nu}, Z_{\mu \gt... \mu_5}$ of the $M$-superalgebra. For $n=2$ we obtain 2080 real non-Abelian bosonic tensorial charges $Z_{\mu\nu}, Z_{\mu_1 \mu_2 \mu_3}, Z_{\mu_1 ... \mu_6}$ which, suitably constrained describe the generalized D=11 octonionic conformal algebra. Further, we consider the supersymmetric extension of this octonionic conformal algebra which can be described as D=11 octonionic superconformal algebra with a total number of 64 real fermionic and 239 real bosonic generators.