We give a systematic description of all warped AdS n and Rn-1,1 backgrounds of M-theory and identify the a priori number of supersymmetries that these backgrounds preserve. In particular, we show that AdSn backgrounds preserve N=2[n/2]k for n ≤ 4 and N=2[n/2]+1 k for 4 < n ≤ 7 supersymmetries while Rn−1,1 backgrounds preserve N=2[n/2]k for n ≤ 4 and N=2[n+1/2]k for 4 < n ≤ 7, supersymmetries. Furthermore for AdS n backgrounds that satisfy the requirements for the maximum principle to hold, we show that the Killing spinors can be identified with the zero modes of Dirac-like operators on M 11−n coupled to fluxes thus establishing a new class of Lichnerowicz type theorems. We also demonstrate that the Killing spinors of generic warped AdS n backgrounds do not factorize into products of Killing spinors on AdS n and Killing spinors on the transverse space.
- Black Holes in String Theory
- Supergravity Models