Revisiting extremal couplings in AdS/CFT

We consider an effective theory of massive scalar fields on a fixed AdS_d+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 CFT_d operators matches the sum of all the others. For cubic bulk couplings, this is ∆_i + ∆_j = ∆_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.