Quantum gravity from conformal field theory

We bootstrap loop corrections to AdS(5) supergravity amplitudes by enforcing the consistency of the known classical results with the operator product expansion of 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 nmltiplets in AdS. Tins in turn yields further new results on subleading O(1/N-4) corrections to certain double-trace anomalous dimensions.