Unitarity and the Holographic S-Matrix

TL;DR

This paper demonstrates that the unitarity of the S-Matrix in flat space can be derived from the conformal block structure of AdS/CFT, introducing new techniques for analyzing conformal field theories and deriving holographic cutting rules.

Contribution

It provides a holographic derivation of the optical theorem and cutting rules using conformal block analysis and introduces new methods for isolating conformal block contributions in CFTs.

Findings

Derived unitarity of the S-Matrix from conformal block behavior.

Introduced a method to extract primary operator contributions in OPE.

Established a relation between conformal block coefficients and anomalous dimensions.

Abstract

The bulk S-Matrix can be given a non-perturbative definition in terms of the flat space limit of AdS/CFT. We show that the unitarity of the S-Matrix, ie the optical theorem, can be derived by studying the behavior of the OPE and the conformal block decomposition in the flat space limit. When applied to perturbation theory in AdS, this gives a holographic derivation of the cutting rules for Feynman diagrams. To demonstrate these facts we introduce some new techniques for the analysis of conformal field theories. Chief among these is a method for conglomerating local primary operators to extract the contribution of an individual primary in their OPE. This provides a method for isolating the contribution of specific conformal blocks which we use to prove an important relation between certain conformal block coefficients and anomalous dimensions. These techniques make essential use of the simplifications that occur when CFT correlators are expressed in terms of a Mellin amplitude.