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

摘要

Following [Phys. Lett. B 539 (2002) 266] we further apply the octonionic structure to supersymmetric D = 11 M-theory. We consider the octonionic 2(n+1) x 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 x 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 x 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(munu), Z(mu)...mu(5) of the M-superalgebra. For n = 2 we obtain 2080 real non-Abelian bosonic tensorial charges Z(munu), Z(mu1mu2mu3), Z(mu1)...mu(6) which, suitably constrained describe the generalized D = 11octonionic conformal algebra. Further, we consider the supersymmetric extension of this octomonic 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. (C) 2003 Published by Elsevier B.V. [References: 25]