Effective AdS/renormalized CFT

Abstract

For an effective AdS theory, we present a simple prescription to compute the renormalization of its dual boundary field theory at \( \mathcal{O}\left( {{{1} \left/ {{{N^2}}} \right.}} \right) \). In particular, we define anomalous dimension holographically as the dependence of the wave-function renormalization factor on the radial cutoff in the Poincare patch of AdS. With this definition, the anomalous dimensions of both single- and double-trace operators are calculated. Three different dualities are considered with the field theory being CFT, CFT with a double-trace deformation and spontaneously broken CFT. For the second dual pair, we compute scaling corrections at the UV and IR fixed points of the RG flow triggered by the double-trace deformation. For the last case, we discuss whether our prescription is sensitive to the AdS interior or equivalently, the IR physics of the dual field theory.