We provide a new general setting for scalar interacting fields on the covering of a (d+1)-dimensional AdS spacetime. The formalism is used at first to construct a one-parameter family of field theories, each living on a corresponding spacetime submanifold of AdS, which is a cylinder Rx Sd-1. We then introduce a limiting procedure which directly produces Lüscher–Mack CFT's on the covering of the AdS asymptotic cone. Our generalized AdS-->CFT construction is nonperturbative, and is illustrated by a complete treatment of two-point functions, the case of Klein–Gordon fields appearing as particularly simple in our context.
We also show how the Minkowskian representation of these boundary CFT's can be directly generated by an alternative limiting procedure involving Minkowskian theories in horocyclic sections (nowadays called (d-1)-branes, 3-branes for AdS5). These theories are restrictions to the brane of the ambient AdS field theory considered. This provides a more general correspondence between the AdS field theory and a Poincaré invariant QFT on the brane, satisfying all the Wightman axioms. The case of two-point functions is again studied in detail from this viewpoint as well as the CFT limit on the boundary.
