Nota de FísicaPublicado
Octonionic M-theory and D=11 Generalized Conformal and Superconformal Algebras
Jerzy Lukierski; F. Toppan
2003
Dados da publicação
- Autores
- Jerzy Lukierski; F. Toppan
- Tipo
- Nota de Física
- Status
- Publicado
- Data de publicação
- 2003
- Descrição
- 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 ($9+n,n$) ($n=0,1,2, \ldots$) 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 $512$ Abelian $O(10,1)$ tensorial charges $Z_\mu$, $Z_{\mu\nu}$, $Z_{\mu \ldots \mu_5}$ of the $M$-superalgebra. For $n=2$ we obtain 2048 real non-Abelian bosonic tensorial charges $Z_{\mu\nu}, Z_{\mu_1 \mu_2 \mu_3}, Z_{\mu_1 \ldots \mu_6}$ 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 %$OSp(1;8|\bf{O})$ with a total number of $64$ real fermionic and $239$ real bosonic generators.
- Ano
- 2003
- Número
- CBPF-NF-001/03
- Vínculo com tese
- Não
- Vínculo com bolsa
- Não