Localization in supergravity and quantum ads4/cft3 holography

TY - JOUR

T1 - Localization in supergravity and quantum ads4/cft3 holography

AU - Dabholkar, Atish

AU - Drukker, Nadav

AU - Gomes, João

PY - 2014/10

Y1 - 2014/10

N2 - 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.

AB - 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.

KW - AdS-CFT Correspondence

KW - Extended Supersymmetry

KW - Models of Quantum Gravity

UR - http://www.scopus.com/inward/record.url?scp=84928580110&partnerID=8YFLogxK

U2 - 10.1007/JHEP10(2014)090

DO - 10.1007/JHEP10(2014)090

M3 - Article

AN - SCOPUS:84928580110

SN - 1126-6708

VL - 2014

SP - 1

EP - 31

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

IS - 10

M1 - 90

ER -