Reversing renormalization-group flows with AdS/CFT

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 consider certain 1/N effects corresponding to quantum field effects in the bulk.