Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2003-07-08
Int.J.Mod.Phys.A18:2135-2144,2003
Physics
High Energy Physics
High Energy Physics - Theory
14 pages, LaTex. Lecture Notes delivered at the II Summer School in Modern Mathematical Physics, Kopaonik (YU), Sept. 2002. In
Scientific paper
10.1142/S0217751X03015581
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.
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