A Comment on the InfraRed 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 infrared 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 $:\phi^4:$. We also give a brief discussion on possible renormalization strategies and the specific problems that arise in this context.
 Publication:

arXiv eprints
 Pub Date:
 September 2007
 arXiv:
 arXiv:0709.4486
 Bibcode:
 2007arXiv0709.4486G
 Keywords:

 Mathematical Physics;
 81T08;
 81T30