All Killing Superalgebras for Warped AdS Backgrounds

Abstract

We present all the symmetry superalgebras $\mathfrak{g}$ of all warped AdS${}_k{\times }_w{M}^{d-k}$, $k>2$, flux backgrounds in $d=10,11$ dimensions preserving any number of supersymmetries. First we give the conditions for $\mathfrak{g}$ to decompose into a direct sum of the isometry algebra of AdS${}_k$ and that of the internal space $M^{d-k}$. Assuming this decomposition, we identify all symmetry superalgebras of AdS${}_3$ backgrounds by showing that the isometry groups of internal spaces act transitively on spheres. We demonstrate that in type II and $d=11$ theories the AdS${}_3$ symmetry superalgebras may not be simple and also present all symmetry superalgebras of heterotic AdS${}_3$ backgrounds. Furthermore, we explicitly give the symmetry superalgebras of AdS${}_k$, $k>3$, backgrounds and prove that they are all classical.

41 pages, latex