Exploring Perturbative Conformal Field Theory in Mellin space

Understand

We explore the Mellin representation of correlation functions in conformal field theories in the weak coupling regime.

• We provide a complete proof for a set of Feynman rules to write the Mellin amplitude for a general tree level Feynman diagram involving only scalar operators.
• We find a factorised form involving beta functions associated to the propagators, similar to tree level Feynman rules in momentum space for ordinary QFTs.
• We also briefly consider the case where a generic scalar perturbation of the free CFT breaks conformal invariance.