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Localization in supergravity and quantum AdS 4 /CFT3 holography

  • Atish Dabholkar
  • Nadav DrukkerEmail author
  • João Gomes
Open Access
Article

Abstract

We compute the quantum gravity partition function of M-theory on AdS 4 ×X 7 by using localization techniques in four-dimensional gauged supergravity obtained by a consistent truncation on the Sasaki-Einstein manifold X 7. 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 AdS 4. 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.

Keywords

Extended Supersymmetry AdS-CFT Correspondence Models of Quantum Gravity 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2014

Authors and Affiliations

  1. 1.Sorbonne Universités, UPMC Paris 06, UMR 7589, LPTHEParisFrance
  2. 2.CNRS, UMR 7589, LPTHEParisFrance
  3. 3.Department of MathematicsKing’s CollegeLondonUK
  4. 4.DAMTP, Center for Mathematical SciencesUniversity of CambridgeCambridgeUK

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