A general construction of conformal field theories from scalar anti-de Sitter quantum field theories

We provide a new general setting for scalar interacting fields on the cover ing 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 cor responding spacetime submanifold of AdS, which is a cylinder R X Sd-1. We t hen introduce a limiting procedure which directly produces Luscher-Mack CFT 's on the covering of the AdS asymptotic cone. Our generalized AdS-->CFT co nstruction is nonperturbative, and is illustrated by a complete treatment o f two-point functions, the case of Klein-Gordon fields appearing as particu larly 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 Minko wskian theories in horocyclic sections (nowadays called (d-1)-branes, 3-bra nes for AdS(5)). These theories are restrictions to the brane of the ambien t AdS field theory considered. This provides a more general correspondence between the AdS field theory and a Poincare invariant QFT on the brane, sat isfying all the Wightman axioms. The case of two-point functions is again s tudied in detail from this viewpoint as well as the CFT limit on the bounda ry. (C) 2000 Elsevier Science B.V. All rights reserved.