Reversing Renormalization-Group Flows with AdS/CFT

TL;DR

This paper explores how non-local boundary conditions in AdS/CFT can reverse the direction of renormalization-group flows, connecting different conformal field theories in a novel way, especially considering quantum effects at large N.

Contribution

It demonstrates that non-local deformations can invert RG flows between CFTs, providing a new perspective on the relationship between bulk boundary conditions and dual field theories.

Findings

Non-local boundary conditions induce non-local RG flows.

Such flows can reverse the direction between UV and IR fixed points.

Quantum effects at large N are crucial in these flows.

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 (CFT_1) to an IR theory (CFT_2), we show that one can find such a non-local flow in which the endpoints are interchanged: the non-local theory flows from CFT_2 in the IR to CFT_1 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.