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Conformal correlators as simplex integrals in momentum space

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We review conformal field theory from a momentum-space perspective, motivated by applications to inflationary cosmology. Our main result is a generalised Feynman integral representation for the general scalar n-point function in any conformal field theory. This integral has the topology of an (n-1)-simplex, where the operators are inserted at the vertices of the simplex and the momenta running in between are the integration variables. The integrand then features an arbitrary function of the n(n-3)/2 conformal cross ratios that can be constructed from these integration variables. We show how this simplex representation solves the conformal Ward identities, and discuss its application to holographic theories. For contact Witten diagrams, the simplex representation can be found using a star-mesh duality from electrical circuit theory.

This talk is part of the Theoretical Physics Colloquium series.

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