Bubbles in AdS

We investigate loop corrections to the four-point function of identical scalar operators in a four-dimensional large N conformal field theory, holographically dual to AdS with a quartic interaction. We focus on the universal part of the correlator that, at any order in 1/N, is completely determined by tree-level data. We show how this contribution controls the part of the anomalous dimensions of double-trace operators, that exhibits a characteristic log ℓ dependence at large spin ℓ. We resum these effects to all orders in 1/N and show that they admit a natural effective description in AdS. Finally, by reformulating the problem in Mellin space, we demonstrate that the same contribution corresponds to consecutive unitarity cuts of bubble diagrams in the flat-space limit.