AdS/CFT boundary conditions, multi-trace perturbations, and the c-theorem

TL;DR

This paper explores boundary conditions in AdS/CFT, analyzing how double-trace perturbations influence RG flow and central charge, revealing a unit shift and novel effects for certain bulk field masses.

Contribution

It provides a detailed calculation of RG flow induced by double-trace perturbations and clarifies discrepancies in previous results related to boundary conditions and field masses.

Findings

RG flow causes a unit shift in central charge

Discovered non-trivial flow for fields at the Breitenlohner-Freedman bound

Clarified discrepancies in earlier AdS/CFT boundary condition results

Abstract

We discuss possible choices for boundary conditions in the AdS/CFT correspondence, and calculate the renormalisation group flow induced by a double-trace perturbation. In running from the UV to the IR there is a unit shift in the central charge. The discrepancy between our result and results obtained by other authors is accounted for by the discovery that there is a non-trivial flow for perturbations induced by bulk fields with masses saturating the Breitenlohner-Freedman bound.