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

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 $Z_{\mu }{Z}_{\mu \nu },Z_{\mu >...{\mu }_5}$ 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.

LateX, 13 pages, corrected some typos, version in press in PLB

References in corpus (4)

• Quaternionic and Octonionic Spinors. A Classification
• Generalized Space-time Supersymmetries, Division Algebras and Octonionic M-theory
• Division Algebras, Extended Supersymmetries and Applications
• Free Fields Equations For Space-Time Algebras With Tensorial Momentum

Cited by in corpus (6)

• Octonionic Electrodynamics
• Geometrical Applications of Split Octonions
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• Generalized non-associative structures on the 7-sphere
• Non-Associativity in the Clifford Bundle on the Parallelizable Torsion 7-Sphere
• Thermal Lie Superalgebras