Reversing Renormalization-Group Flows with AdS/CFT
Abstract
For scalar fields in AdS with masses slightly above the Breitenlohner-Freedman bound, appropriate non-local boundary conditions can define a unitary theory. Such boundary conditions correspond to non-local deformations of the dual CFT, and generate a non-local renormalization-group flow. Nevertheless, a bulk analysis suggests that certain such flows lead to local CFTs in the infra-red. Since the flows are non-local, they can either increase or decrease the central charge of the CFT. In fact, given any local renormalization-group flow within a certain general class which leads from a UV theory (CFT1) to an IR theory (CFT2), we show that one can find such a non-local flow in which the endpoints are interchanged: the non-local theory flows from CFT2 in the IR to CFT1 in the UV. We work at large N, but the flows we consider involve quantum field effects in the bulk, corresponding to 1/N corrections in the dual theory.