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arXiv · 1607.07334

Exploring Perturbative Conformal Field Theory in Mellin space

Amin A. Nizami·Arnab Rudra·Sourav Sarkar·Mritunjay Verma
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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.

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Amin A. Nizami, Arnab Rudra, Sourav Sarkar, Mritunjay Verma. 2016-07-25. Exploring Perturbative Conformal Field Theory in Mellin space. https://doi.org/10.1007/jhep01(2017)102

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