All Killing Superalgebras for Warped AdS Backgrounds

We present all the symmetry superalgebras of all warped AdS_k ×_w M^d−k, k>2, flux backgrounds in d=10,11 dimensions preserving any number of supersymmetries. First we give the conditions for to decompose into a direct sum of the isometry algebra of AdSk and that of the internal space Md−k. Assuming this decomposition, we identify all symmetry superalgebras of AdS3 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 AdS3 symmetry superalgebras may not be simple and also present all symmetry superalgebras of heterotic AdS3 backgrounds. Furthermore, we explicitly give the symmetry superalgebras of AdSk, k>3, backgrounds and prove that they are all classical