The algebraic structure of cut Feynman integrals and the diagrammatic coaction
(2017) Physical Review Letters — Vol. 119, p. 51601 (2017)
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- Abstract
- We study the algebraic and analytic structure of Feynman integrals by proposing an operationthat maps an integral into pairs of integrals obtained from a master integrand and a correspondingmaster contour. This operation is a coaction. It reduces to the known coaction on multiple poly-logarithms, but applies more generally, e.g. to hypergeometric functions. The coaction also appliesto generic one-loop Feynman integrals with any configuration of internal and external masses, andin dimensional regularization. In this case, we demonstrate that it can be given a diagrammaticrepresentation purely in terms of operations on graphs, namely contractions and cuts of edges.The coaction gives direct access to (iterated) discontinuities of Feynman integrals and facilitatesa straightforward derivation of the differential equations they admit. In particular, the differen-tial equations for any one-loop integral are determined by the diagrammatic coaction using limitedinformation about their maximal, next-to-maximal, and next-to-next-to-maximal cuts.
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Duhr, C., & et al. (2017). The algebraic structure of cut Feynman integrals and the diagrammatic coaction. Physical Review Letters, 119, 51601. https://doi.org/10.1103/PhysRevLett.119.051601 (Original work published 2017)