On Feynman rules for Mellin amplitudes in AdS/CFT

TL;DR

This paper derives Feynman rules for Mellin amplitudes in AdS/CFT scalar theories by explicitly evaluating Witten diagrams, confirming their consistency with flat space Feynman rules in the appropriate limit.

Contribution

It provides a direct derivation of Mellin space Feynman rules from Witten diagram integrals, clarifying their origin and validity.

Findings

Derived Mellin Feynman rules from Witten diagrams.

Confirmed rules reduce to flat space Feynman rules in the flat limit.

Validated the rules for scalar phi^n theory.

Abstract

The computation of CFT correlation functions via Witten diagrams in AdS space can be simplified via the Mellin transform. Recently a set of Feynman rules for tree-level Mellin space amplitudes has been proposed for scalar theories. In this note we derive these rules by explicitly evaluating all of the relevant Witten diagram integrals for the scalar phi^n theory. We also check that the rules reduce to the usual Feynman rules in the flat space limit.