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

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.

Figures (2)

• Figure 1: The standard CFT$_{d}$ scalar exchange graph. The solid lines represent the full propagator of ${\cal O}(x)$, the dotted line represents the full propagator of $\sigma(x)$ and the dark blobs stand for the full vertex functions ruehl1tassos1.
• Figure 2: The AdS$_{d+1}$ scalar exchange graph. The solid lines represent the "bulk-to-boundary" propagator of ${\cal O}(x)$ and the dotted line represents the standard "bulk-to-bulk" propagator of $\sigma(x)$freedman1.