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 $ \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.