Revisiting Extremal Couplings in AdS/CFT

Abstract

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 $\hat{I}{”}_i+\hat{I}{”}_j=\hat{I}{”}_k$. 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.

20 pages + appendices, matches published version