Effective AdS/renormalized CFT

TL;DR

This paper introduces a straightforward holographic method to compute the renormalization and anomalous dimensions of operators in dual boundary theories within the AdS/CFT framework, including various dualities and RG flows.

Contribution

It provides a simple prescription for holographic renormalization and anomalous dimension calculation applicable to multiple dualities involving AdS and CFTs.

Findings

Calculated anomalous dimensions for single- and double-trace operators.

Analyzed scaling corrections at UV and IR fixed points of RG flow.

Discussed the sensitivity of the prescription to IR physics and the AdS interior.

Abstract

For an effective AdS theory, we present a simple prescription to compute the renormalization of its dual boundary field theory. 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.