Physics NotePublished
Generalized Space-time Supersymmetries, Division Algebras and Octonionic M-theory
Jerzy Lukierski; F. Toppan
2002
Publication details
- Authors
- Jerzy Lukierski; F. Toppan
- Type
- Physics Note
- Status
- Published
- Publication date
- 2002
- Description
- We describe the set of generalized Poincar\'{e} and conformal superalgebras in $D=4,5$ and $7$ dimensions as two sequences of superalgebraic structures, taking values in the division algebras ${\bf R},{\bf C}$ and ${\bf H}$. The generalized conformal superalgebras are described for $D=4$ by $OSp(1;8|{\bf R})$, for $D=5$ by $SU(4,4;1)$ and for $D=7$ by $U_\alpha U(8;1|{\bf H})$. The relation with other schemes, in particular the framework of conformal spin (super)algebras and Jordan (super)algebras is discussed. By extending the division-algebra-valued superalgebras to octonions we get in $D=11$ an octonionic generalized Poincar\'{e} superalgebra, which we call {\em octonionic M-algebra}, describing the octonionic M-theory. It contains 32 real supercharges but, due to the octonionic structure, only $52$ real bosonic generators remain independent in place of the $528$ bosonic charges of standard $M$-algebra. In octonionic M-theory there is a sort of equivalence between the octonionic M2 (supermembrane) and the octonionic M5 (super-$5$-brane) sectors. We also define the octonionic generalized conformal M-superalgebra, with $239$ bosonic generators.
- Year
- 2002
- Number
- CBPF-NF-001/02
- Linked to a thesis
- No
- Linked to a grant
- No