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Humboldt-Universität zu Berlin - Mathematisch-Naturwissenschaftliche Fakultät - Institut für Mathematik

Preprint 2016-14



Amin A. Nizami, Arnab Rudra, Sourav Sarkar and Mritunjay Verma


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.

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 2016-14


47 pp.