## Abstract

Abstract: We identify the fractions of supersymmetry preserved by the most general warped flux AdS and flat backgrounds in both massive and standard IIA supergravities. We find that AdS<inf>n</inf> × <inf>w</inf>M<sup>10 − n</sup> preserve 2<sup>n/2</sup>k for n ≤ 4 and 2<sup>[n/2]+1</sup>k for 4 < n ≤ 7 supersymmetries, k ∈ ℕ<inf>>0</inf>. In addition we show that, for suitably restricted fields and M<sup>10 − n</sup>, the killing spinors of AdS backgrounds are given in terms of the zero modes of Dirac like operators on M<sup>10 − n</sup>. This generalizes the Lichnerowicz theorem for connections whose holonomy is included in a general linear group. We also adapt our results to ℝ<sup>1,n − 1</sup> × <inf>w</inf>M<sup>10 − n</sup> backgrounds which underpin flux compactifications to ℝ<sup>1,n − 1</sup> and show that these preserve 2<sup>n/2</sup>k for 2<n≤42,<sup>n+1/2</sup>k for 4 < n ≤ 8, and 2<sup>n2</sup>k for n = 9, 10 supersymmetries.

Original language | English |
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Article number | 135 |

Journal | Journal of High Energy Physics |

Volume | 2015 |

Issue number | 9 |

DOIs | |

Publication status | Published - 29 Sept 2015 |

## Keywords

- AdS-CFT Correspondence
- Supergravity Models