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.

37 pages, latex

References in corpus (3)

• AdS_6 solutions of type II supergravity
• Comments on AdS2 solutions of D=11 Supergravity
• N=31, D=11

Cited by in corpus (10)

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• Supersymmetric Backgrounds, the Killing Superalgebra, and Generalised Special Holonomy
• Supersymmetry of AdS and flat IIB backgrounds
• Infinitesimal moduli of G2 holonomy manifolds with instanton bundles
• Non-integrability in AdS${}_3$ vacua
• On supersymmetric Anti-de-Sitter, de-Sitter and Minkowski flux backgrounds
• Supersymmetric $d{S}_n$ solutions for $n\ge 5$ in $D=11$ supergravity
• Supersymmetric dS4 solutions in D=11 supergravity
• The TCFHs of D=11 AdS backgrounds and hidden symmetries
• Decomposable $(5,6)$-solutions in eleven-dimensional supergravity