M-theory backgrounds with 30 Killing spinors are maximally supersymmetric

@article{Gran2010MtheoryBW,
  title={M-theory backgrounds with 30 Killing spinors are maximally supersymmetric},
  author={Ulf Gran and J. B. Gutowski and George Papadopoulos},
  journal={Journal of High Energy Physics},
  year={2010},
  volume={2010},
  pages={1-38}
}
We show that all M-theory backgrounds which admit more than 29 Killing spinors are maximally supersymmetric. In particular, we find that the supercovariant curvature of all backgrounds which preserve 30 supersymmetries, subject to field equations and Bianchi identities, vanishes, and that there are no such solutions which arise as discrete quotients of maximally supersymmetric backgrounds. 

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