Conformal invariance arises in a variety of physical contexts, from fixed points of renormalisation group flows to correlation functions in inflationary cosmology. As is well known, conformal invariance places powerful constraints on the properties of a theory, and completely determines the form of 2- and 3-point correlation functions up to only a few constants. In this talk, we re-examine this story from the perspective of momentum space. From a first principles analysis of the conformal Ward identities, we derive the general form of CFT 2- and 3-point functions in momentum space. For specific operator and spacetime dimensions, we show renormalisation is required leading to novel conformal anomalies and beta functions. These results have potential applications to condensed matter physics and cosmology, which we illustrate with a discussion of inflationary correlators in de Sitter spacetime.

Part of the joint Relativity/Cosmology/Strings seminar series.