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

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.