Scattering in Anti-de Sitter Space and Operator Product Expansion

TL;DR

This paper develops a formalism for evaluating scalar exchange diagrams in AdS space, revealing their connection to conformal partial waves and identifying contributions from bound states, with implications for AdS/CFT correspondence.

Contribution

It introduces a new method to compute AdS exchange diagrams as conformal partial waves, including contributions from bound states, and clarifies the structure of four-point functions in AdS/CFT.

Findings

Amplitude expressed as a power series in cross-ratios

Logarithmic singularities linked to operator dimensions

Identification of bound state contributions in AdS

Abstract

We develop a formalism to evaluate generic scalar exchange diagrams in AdS_{d+1} relevant for the calculation of four-point functions in AdS/CFT correspondence. The result may be written as an infinite power series of functions of cross-ratios. Logarithmic singularities appear in all orders whenever the dimensions of involved operators satisfy certain relations. We show that the AdS_{d+1} amplitude can be written in a form recognisable as the conformal partial wave expansion of a four-point function in CFT_{d} and identify the spectrum of intermediate operators. We find that, in addition to the contribution of the scalar operator associated with the exchanged field in the AdS diagram, there are also contributions of some other operators which may possibly be identified with two-particle bound states in AdS. The CFT interpretation also provides a useful way to ``regularize'' the logarithms appearing in AdS amplitude.