All Killing Superalgebras for Warped AdS Backgrounds

Understand

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.