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

TL;DR

This paper constructs a non-perturbative extension of the super-isometry algebra for the AdS_7xS^4 background in M-theory, revealing a complex algebraic structure with new charges and non-commuting elements.

Contribution

It introduces a novel method to extend the super-isometry algebra directly by solving Jacobi identities, without embedding into a larger superalgebra.

Findings

Extended algebra includes new non-perturbative charges.

Charges appear in {Q,Q} brackets via linear combinations with bosonic generators.

The algebra reduces correctly to flat-space limit but is non-simple and non-commutative.

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.