Feynman Diagrams from Conformal Integrals

TL;DR

This paper demonstrates that momentum space Feynman diagrams with massless internal fields can be represented as conformal integrals, enabling exact computation of entire families of diagrams using conformal symmetry.

Contribution

It introduces a classification of Feynman diagrams into conformal families and shows how to compute all diagrams in a family from a single conformal integral.

Findings

Exact solutions for some conformal integrals are used to solve related Feynman diagrams.

All orders in regularization parameter are addressed for finite or regularized diagrams.

Feynman diagrams are systematically categorized into conformal families for efficient computation.

Abstract

We show that momentum space Feynman diagrams involving internal massless fields can be cast as conformal integrals. This leads to a classification of all Feynman diagrams into conformal families, labelled by conformal integrals. Computing the conformal integral in each family suffices to compute all the Feynman diagrams in the family exactly. Using known exact results for some conformal integrals, we present the solutions to the other Feynman diagrams in the corresponding families. These are answers to either finite or dimensionally regularized Feynman diagrams to all orders in the regularization parameter.