All Killing Superalgebras for Warped AdS Backgrounds

TL;DR

This paper classifies all symmetry superalgebras of warped AdS backgrounds in 10 and 11 dimensions, revealing their structure, conditions for decomposition, and explicit forms for various AdS$_k$ cases, including heterotic backgrounds.

Contribution

It provides a comprehensive classification of all symmetry superalgebras for warped AdS backgrounds, including conditions for decomposition and explicit algebra structures for different dimensions.

Findings

All symmetry superalgebras for warped AdS backgrounds are classified.

Conditions for superalgebra decomposition into isometry parts are established.

Explicit superalgebras for AdS$_k$, $k>3$, backgrounds are derived.

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.