On the Octonionic M-superalgebra
Abstract
Description
The generalized supersymmetries admitting abelian bosonic tensorial central charges are classified in accordance with their division algebra structure (over ${\bf R}$, ${\bf C}$, ${\bf H}$ or ${\bf O}$). It is shown in particular that in D=11 dimensions, the $M$-superalgebra admits a consistent octonionic formulation, involving 52 real bosonic generators (in place of the 528 of the standard $M$-superalgebra). The octonionic $M5$ (super-5-brane) sector coincides with the octonionic $M1$ and $M2$ sectors, while in the standard formulation these sectors are all independent. The octonionic conformal and superconformal $M$-algebras are explicitly constructed. They are respectively given by the $Sp(8|{\bf O})$ ($OSp(1,8|{\bf O})$) (super)algebra of octonionic-valued (super)matrices, whose bosonic subalgebra consists of 232 (and respectively 239) generators.
17 pages. Proceedings of the Workshop on Integrable Theories, Solitons and Duality, S. Paulo, July 2002. In JHEP
17 pages. Proceedings of the Workshop on Integrable Theories, Solitons and Duality, S. Paulo, July 2002. In JHEP