Journal Article

Airy function and 4d quantum gravity

Hirano, Shinji, Caputa, Paweł

2018

Overview

A bstract We study four-dimensional quantum gravity with negative cosmological constant in the minisuperspace approximation and compute the partition function for the S 3 boundary geometry. In this approximation scheme the path integrals become dominated by a class of asymptotically AdS “microstate geometries.” Despite the fact that the theory is pure Einstein gravity without supersymmetry, the result precisely reproduces, up to higher curvature corrections, the Airy function in the S 3 partition function of the maximally supersymmetric Chern-Simons-matter (CSM) theory which sums up all perturbative 1 /N corrections. We also show that this can be interpreted as a concrete realization of the idea that the CFT partition function is a solution to the Wheeler-DeWitt equation as advocate in the holographic renormalization group. Furthermore, the agreement persists upon the inclusion of a string probe and it reproduces the Airy function in the vev of half-BPS Wilso loops in the CSM theory. These results may suggest that the supergravity path integrals localize to the minisuperspace in certain cases and the use of the minisuperspace approximation in AdS/CFT may be a viable approach to study 1 /N corrections to large N CFTs.

• Publisher: Springer Berlin Heidelberg,Springer Nature B.V,SpringerOpen
• Subject: AdS-CFT Correspondence / Airy function / Approximation / Classical and Quantum Gravitation / Cosmological constant / Curvature / Elementary Particles / High energy physics / Integrals / Mathematical analysis / Models of Quantum Gravity / Partitions / Partitions (mathematics) / Physics / Physics and Astronomy / Quantum Field Theories / Quantum Field Theory / Quantum gravity / Quantum Physics / Regular Article - Theoretical Physics / Relativity Theory / String Theory / Supergravity / Supersymmetry