A note on the analyticity of AdS scalar exchange graphs in the crossed channel

TL;DR

This paper investigates the analytic structure of AdS scalar exchange graphs in the crossed channel, demonstrating that non-analytic terms cancel out due to hypergeometric function properties, which supports the operator product expansion in AdS/CFT.

Contribution

It reveals the cancellation of non-analytic terms in AdS scalar exchange graphs, establishing a key condition for the operator product expansion in AdS/CFT correspondence.

Findings

Non-analytic terms in AdS scalar exchange graphs cancel out.

Hypergeometric function properties ensure analyticity.

Supports the validity of the operator product expansion in AdS/CFT.

Abstract

We discuss the analytic properties of AdS scalar exchange graphs in the crossed channel. We show that the possible non-analytic terms drop out by virtue of non-trivial properties of generalized hypergeometric functions. The absence of non-analytic terms is a necessary condition for the existence of an operator product expansion for CFT amplitudes obtained from AdS/CFT correspondence.