Exploring Perturbative Conformal Field Theory in Mellin space

Abstract

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. Mellin space still has some utility and one can consider non-conformal Mellin representations. In this context, we find that the beta function corresponding to conformal propagator uplifts to a hypergeometric function.

47 pages, 15 figures

References in corpus (6)

• Writing CFT correlation functions as AdS scattering amplitudes
• Spinning AdS Propagators
• D-independent representation of Conformal Field Theories in D dimensions via transformation to auxiliary Dual Resonance Models. Scalar amplitudes
• Four point function of $\mathcal{N}=4$ stress-tensor multiplet at strong coupling
• D-dimensional Conformal Field Theories with anomalous dimensions as Dual Resonance Models
• Lessons from crossing symmetry at large N

Cited by in corpus (3)

• TASI lectures on AdS/CFT
• A Note on (Non)-Locality in Holographic Higher Spin Theories
• Mellin-(Schwinger) representation of One-loop Witten diagrams in AdS