Conformal 4-point functions in momentum space

Authors: Adam Bzowski, Paul McFadden, Kostas Skenderis

Preprint-number: UUITP-43/19

We provide a Feynman integral representation for the general momentum-space scalar 4-point function in any conformal field theory. This representation solves the conformal Ward identities and features an arbitrary function of two variables which play the role of momentum-space conformal cross-ratios. It involves three integrations over momenta (i.e., is 3-loop like), though in certain cases the number of integrations reduces to two or one. We identify the special values of the operator and spacetime dimensions for which singularities arise leading to anomalies and beta functions. Several illustrative examples from perturbative field theory and holography are discussed.