Quantum Gravity from Conformal Field Theory

TL;DR

This work uses a conformal bootstrap approach to quantum gravity in AdS5 by leveraging the N=4 SYM OPE to bootstrap loop corrections to AdS5 supergravity. By analyzing four-point functions of half-BPS operators and their double-trace spectrum, the authors determine leading and subleading corrections to double-trace anomalous dimensions and predict the one-loop four-graviton amplitude in AdS, expressed through single-valued polylogarithms and ladder integrals. They derive explicit twist-4 anomalous dimensions at order a^2 and show that the spin-analyticity constraint fixes the one-loop amplitude up to a controlled ambiguity, which they set to zero. The results provide concrete, testable data for AdS/CFT at the quantum gravity level and establish a framework for extracting higher-order corrections from CFT data.

Abstract

We bootstrap loop corrections to AdS${}_5$ supergravity amplitudes by enforcing the consistency of the known classical results with the operator product expansion of $\mathcal{N}=4$ super Yang-Mills theory. In particular this yields much new information on the spectrum of double-trace operators which can then be used, in combination with superconformal symmetry and crossing symmetry, to obtain a prediction for the one-loop amplitude for four graviton multiplets in AdS. This in turn yields further new results on subleading $O(1/N^4)$ corrections to certain double-trace anomalous dimensions.