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.
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Steven B. Giddings (1999) studied this question.
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