AdS/CFT correspondence: lessons from constructive field theory

Following ideas of Dütsch and Rehren, we give a proof of the equivalence of the two prescriptions of the conformal boundary field in AdS/CFT ("duality"). We use rigorous Euclidean path integrals to define functional delta functions of boundary values and restrictions to the conformal boundary. Both, in the interacting and non-interacting case, divergences arise that have not been observed so far. These divergences can, however, be removed without doing damage to reflection positivity and symmetry. Interactions with IR cut-off are taken into account in D=2 dimensional Euclidean AdS. We comment on some intriguing novel features of the IR-problem which comes from the fact that boundary sources in AdS/CFT lead to shifts in the bulk interaction that create an infinite amount of energy.

This talk is based on joint work with Horst Thaler, math-ph/0611006.