Conformal field theory in momentum space

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Paul McFadden (Newcastle)

28 November 2018

Conformal symmetry places strong constraints on the properties of a quantum field theory, fixing the form of all 2- and 3-point functions up to constants. The resulting expressions are well-known in position space, yet surprisingly their counterparts in momentum space have only recently been identified.

We review these developments, introducing an elementary method for solving the momentum-space conformal Ward identities. In special cases, divergences arise and we must renormalise giving rise to beta functions and anomalies.

Our results have interesting new applications ranging from condensed matter physics to holographic cosmology.