Four Point Functions of the Stress Tensor and Conserved Currents in AdS₄/CFT₃

We compute four point functions of the stress tensor in AdS4/CFT3. We bypass the tedious evaluation of Witten diagrams by using the analytic properties of the correlators. In this method, the four point function is obtained as the sum of residues of a rational function at easily identifiable poles. We verify that these correlators have the correct flat space limit and the 4 dimensional graviton amplitude appears as the coefficient of a specified singularity in the correlator. Our results suggest that double trace operators of the stress tensor, in theories with a pure gravity dual, do not develop anomalous dimensions at leading order in 1/N.