Localization in supergravity and quantum ads4/cft3 holography

Atish Dabholkar, Nadav Drukker, João Gomes

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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 languageEnglish
Article number90
Pages (from-to)1-31
JournalJournal of High Energy Physics
Issue number10
Early online date1 Oct 2014
Publication statusPublished - Oct 2014


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


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