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Abstract

Motivated by the study of branes in curved backgrounds, we investigate the construction of central extensions of the super-isometry algebra osp (8|4) of the AdS7×S4 background of M-theory. This algebra is not a subalgebra of osp(1|32) and its central 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 Jacobi identities. This requires, in addition to the expected central charges, the introduction of new ones which appear in the {Q,Q} commutator 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 central 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.