BoundarySMatrix and the Anti–de Sitter Space to Conformal Field Theory Dictionary

Abstract

An $S$ matrix analog is defined for anti–de Sitter (Ads) space by constructing “in” and “out” states that asymptote to the timelike boundary. A derivation parallel to that of the Lehmann-Symanzik-Zimmermann formula shows that this “boundary $S$ matrix” is given directly by correlation functions in the boundary conformal theory. This provides a key entry in the AdS to conformal field theory dictionary.