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arXiv · 1406.0505

Localization in Supergravity and Quantum $AdS_4/CFT_3$ Holography

Atish Dabholkar·Nadav Drukker·Joao Gomes
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Abstract

We compute the quantum gravity partition function of M-theory on $AdS_4 \times 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.

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Atish Dabholkar, Nadav Drukker, Joao Gomes. 2014-09-23. Localization in Supergravity and Quantum $AdS_4/CFT_3$ Holography. https://doi.org/10.1007/jhep10(2014)090

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