Abstract:

After a brief review of conformal theories and the conformal bootstrap, we discuss the Mellin representation of correlation functions for conformal field theories. We consider the Mellin amplitude for a general tree level Feynman diagram for a weakly coupled CFT involving scalar fields and find a factorised form involving beta functions associated to the propagators, similar to tree level Feynman rules in momentum space for ordinary QFTs. We discuss the extension to loop level and, time permitting, briefly comment on unitarity and cutting rules for Mellin amplitudes. We also present results on the leading order anomalous dimensions of a class of composite primary operators in the epsilon expansion for the Gross-Neveu CFT and comment on extending the computations using Mellin space.