Supersymmetry of AdS and flat backgrounds in M-theory

Abstract

We give a systematic description of all warped $Ad{S}_n$ 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 $Ad{S}_n$ backgrounds preserve $N=2^{[\frac{n}{2}]}k$ for $n\le 4$ and $N=2^{[\frac{n}{2}]+1}k$ for $4<n\le 7$ supersymmetries while ${\mathbb{R}}^{n-1,1}$ backgrounds preserve $N=2^{[\frac{n}{2}]}k$ for $n\le 4$ and $N=2^{[\frac{n+1}{2}]}k$ for $4<n\le 7$, supersymmetries. Furthermore for $Ad{S}_n$ 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 $Ad{S}_n$ backgrounds do not factorize into products of Killing spinors on $Ad{S}_n$ and Killing spinors on the transverse space.

arXiv comment37 pages, latex

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• Consistent truncations of supergravity and $\frac{1}{2}$-BPS RG flows in $4d$ SCFTs
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• A class of non-geometric M-theory compactification backgrounds
• Supersymmetric dS4 solutions in D=11 supergravity
• The TCFHs of D=11 AdS backgrounds and hidden symmetries
• A uniqueness theorem for warped $N>16$ Minkowski backgrounds with fluxes
• Decomposable $(5,6)$-solutions in eleven-dimensional supergravity