Abstract
We give a systematic description of all warped AdS n and \( {\mathbb{R}}^{n-1,1} \) backgrounds of M-theory and identify the a priori number of supersymmetries that these backgrounds preserve. In particular, we show that AdS n backgrounds preserve \( N={2}^{\left[\frac{n}{2}\right]}k \) for n ≤ 4 and \( N={2}^{\left[\frac{n}{2}\right]+1}k \) for 4 < n ≤ 7 supersymmetries while \( {\mathbb{R}}^{n-1,1} \) backgrounds preserve \( N={2}^{\left[\frac{n}{2}\right]}k \) for n ≤ 4 and \( N={2}^{\left[{\scriptscriptstyle \frac{n+1}{2}}\right]}k \) 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.
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Gutowski, J., Papadopoulos, G. Supersymmetry of AdS and flat backgrounds in M-theory. J. High Energ. Phys. 2015, 145 (2015). https://doi.org/10.1007/JHEP02(2015)145
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DOI: https://doi.org/10.1007/JHEP02(2015)145