## Abstract

We compute the quantum gravity partition function of M-theory on AdS4×X7 by using localization techniques in four-dimensional gauged supergravity obtained by a consistent truncation on the Sasaki-Einstein manifold X7. The supergravity path integral reduces to a finite dimensional integral over two collective coordinates that parametrize the localizing instanton solutions. The renormalized action of the off-shell instanton solutions depends linearly and holomorphically on the “square root” prepotential evaluated at the center of AdS4. The partition function resembles the Laplace transform of the wave function of a topological string and with an assumption about the measure for the localization integral yields an Airy function in precise agreement with the computation from the boundary ABJM theory on a 3-sphere. Our bulk quantum gravity computation is nonperturbatively exact in four-dimensional Planck length but ignores corrections due to brane-instantons.

Original language | English |
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Article number | 90 |

Pages (from-to) | 1-31 |

Journal | Journal of High Energy Physics |

Volume | 2014 |

Issue number | 10 |

Early online date | 1 Oct 2014 |

DOIs | |

Publication status | Published - Oct 2014 |

## Keywords

- AdS-CFT Correspondence
- Extended Supersymmetry
- Models of Quantum Gravity