On non-perturbative extensions of anti-de-Sitter algebras

Abstract

Motivated by the study of branes in curved backgrounds, we investigate the construction of non-perturbative extensions of the super-isometry algebra osp*(8|4) of the AdS_7xS^4 background of M-theory. This algebra is not a subalgebra of osp(1|32) and its non-perturbative extension can therefore not be obtained by embedding in this simple superalgebra. We show how, instead, it is possible to construct an extension directly by solving the Jacobi identities. This requires, in addition to the expected non-perturbative charges, the introduction of new charges which appear in the {Q,Q} bracket only via a linear combination with the bosonic generators of the isometry algebra. The resulting extended algebra has the correct flat-space limit, but it is not simple and the non-perturbative charges do not commute with the super-isometry generators. We comment on the consequences of this structure for the representation theory and on possible alternatives to our construction.

arXiv comment1+17 pages, textual changes to improve clarity, typos corrected

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• Extensions of AdS_5 x S^5 and the Plane-wave Superalgebras and Their Realization in the Tiny Graviton Matrix Theory
• BPS preons and the AdS-M-algebra
• Topological BPS charges in 10 and 11-dimensional supergravity
• Noncommutative D-brane from Covariant AdS Superstring