We present a systematic description of all warped AdS n × w M 10−n and Rn−1,1×wM10−n IIB backgrounds and identify the a priori number of supersymmetries N preserved by these solutions. In particular, we find that the AdS n backgrounds preserve N=2[n2]k for n ≤ 4 andN=2[n2]+1k for 4 < n ≤ 6 supersymmetries and for k∈N+ suitably restricted. In addition under some assumptions required for the applicability of the maximum principle, we demonstrate that the Killing spinors of AdS n backgrounds can be identified with the zero modes of Dirac-like operators on M 10−n establishing a new class of Lichnerowicz type theorems. Furthermore, we adapt some of these results to Rn−1,1×wM10−n backgrounds with fluxes by taking the AdS radius to infinity. We find that these backgrounds preserve N=2[n2]k for 2 < n ≤ 4 and N=2[n+12]k for 4 < n ≤ 7 supersymmetries. We also demonstrate that the Killing spinors of AdS n × w M 10−n do not factorize into Killing spinors onAdS n and Killing spinors on M 10−n .
- AdS-CFT Correspondence
- Supergravity Models