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Article
Report number	arXiv:2207.07843 ; CERN-TH-2022-122 ; BONN-TH-2022-18
Title	The Diagrammatic Coaction
Author(s)	Gardi, Einan (Edinburgh U.) ; Abreu, Samuel (CERN ; Edinburgh U.) ; Britto, Ruth (Trinity Coll., Dublin) ; Duhr, Claude (Bonn U.) ; Matthew, James (Edinburgh U.)
Publication	2022-10-20
Imprint	2022-07-16
Number of pages	19
Note	19 pages, Talk presented at Loop and Legs in Quantum Field Theory - LL2022, 25-30 April, 2022, Ettal, Germany
In:	PoS LL2022 (2022) 015
In:	16th DESY Workshop on Elementary Particle Physics: Loops and Legs in Quantum Field Theory 2022, Ettal, Germany, 25 - 30 Apr 2022, pp.015
DOI	10.22323/1.416.0015
Subject category	Particle Physics - Phenomenology ; Particle Physics - Theory
Abstract	The diagrammatic coaction underpins the analytic structure of Feynman integrals, their cuts and the differential equations they admit. The coaction maps any diagram into a tensor product of its pinches and cuts. These correspond respectively to differential forms defining master integrals, and integration contours which place a subset of the propagators on shell. In a canonical basis these forms and contours are dual to each other. In this talk I review our present understanding of this algebraic structure and its manifestation for dimensionally-regularized Feynman integrals that are expandable to polylogarithms around integer dimensions. Using one- and two-loop integral examples, I will explain the duality between forms and contours, and the correspondence between the local coaction acting on the Laurent coefficients in the dimensional regulator and the global coaction acting on generalised hypergeometric functions.
Copyright/License	preprint: (License: CC BY 4.0) publication: © 2022-2025 The authors (License: CC-BY-NC-ND-4.0)

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