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Journal Article

Exploring Perturbative Conformal Field Theory in Mellin space


Sarkar,  Sourav
AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Nizami, A. A., Rudra, A., Sarkar, S., & Verma, M. (2017). Exploring Perturbative Conformal Field Theory in Mellin space. Journal of high energy physics: JHEP, 2017(01): 102. doi:10.1007/JHEP01(2017)102.

Cite as: https://hdl.handle.net/11858/00-001M-0000-002B-5FB2-A
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.