Quantum Field Theory in AdS Space instead of Lehmann-Symanzik-Zimmerman Axioms
Balt C. van Rees (CPHT, CNRS, Ecole Polytechnique, Institut Polytechnique de Paris, Route de Saclay, 91128 Palaiseau, France); Xiang Zhao (CPHT, CNRS, Ecole Polytechnique, Institut Polytechnique de Paris, Route de Saclay, 91128 Palaiseau, France, Fields and String Laboratory, Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL), Rte de la Sorge, BSP 728, CH-1015 Lausanne, Switzerland)
The boundary correlation functions for a quantum field theory (QFT) in a fixed anti–de Sitter (AdS) background should reduce to -matrix elements in the flat-space limit. We consider this procedure in detail for four-point functions. With minimal assumptions we rigorously show that the resulting -matrix element obeys a dispersion relation, the nonlinear unitarity conditions, and the Froissart-Martin bound. QFT in AdS thus provides an alternative route to fundamental QFT results that normally rely on the LSZ axioms.
