Supersymmetry of AdS and flat IIB backgrounds

Abstract

We present a systematic description of all warped AdSn ×wM10−n and (Formula Presented.) IIB backgrounds and identify the a priori number of supersymmetries N preserved by these solutions. In particular, we find that the AdSn backgrounds preserve (Formula Presented.) for n ≤ 4 and (Formula Presented.) for 4 < n ≤ 6 supersymmetries and for (Formula Presented.) suitably restricted. In addition under some assumptions required for the applicability of the maximum principle, we demonstrate that the Killing spinors of AdSn backgrounds can be identified with the zero modes of Dirac-like operators on M10−n establishing a new class of Lichnerowicz type theorems. Furthermore, we adapt some of these results to (Formula Presented.) backgrounds with fluxes by taking the AdS radius to infinity. We find that these backgrounds preserve (Formula Presented.) for 2 < n ≤ 4 and (Formula Presented.) for 4 < n ≤ 7 supersymmetries. We also demonstrate that the Killing spinors of AdSn ×wM10−n do not factorize into Killing spinors on AdSn and Killing spinors on M10−n.