A Comment on the Infra-Red Problem in the AdS/CFT Correspondence

Details A Comment on the Infra-Red Problem in the AdS/CFT Correspondence A Comment on the Infra-Red Problem in the AdS/CFT Correspondence

2007-09-27

arxiv.org/abs/0709.4486v1

Physics

Mathematical Physics

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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 ultra-violet 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.

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