Revisiting extremal couplings in AdS/CFT

We consider an effective theory of massive scalar fields on a fixed AdSd+1 background with a cubic extremal interaction among them. A bulk coupling is called extremal whenever the corresponding conformal dimension of any of the dual CFTd operators matches the sum of all the others. For cubic bulk couplings, this is triangle i + triangle j = triangle k. These bulk interactions are often disregarded in the literature since they do not appear in traditional models of AdS/CFT. Turning them on yields a divergent vertex in the dual CFT, and here we show that these divergences can be regulated. Once renormalized, we demonstrate that this coupling introduces non-trivial mixing between single- and double-trace operators, and we compute the anomalous dimensions of the corrected operators to leading order in perturbation theory.