A comment on the infra-red problem in the AdS/CFT correspondence

Abstract

In this note we report on some recent progress in proving the AdS/CFT correspondence for quantum fields using rigorously defined Euclidean path integrals. We also comment on the infra-red problem in the AdS/CFT correspondence and argue that it is different from the usual IR problem in constructive quantum field theory. To illustrate this, a triviality proof based on hypercontractivity estimates is given for the case of an ultraviolet regularized potential of type: φ4:. We also give a brief discussion on possible renormalization strategies and the specific problems that arise in this context. © 2009 Birkhäuser Verlag Basel/Switzerland.