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.
|Number of pages||19|
|Publication status||Accepted/In press - 20 Jul 2022|
|Event||16th DESY Workshop on Elementary Particle Physics: Loops and Legs in Quantum Field Theory 2022 - Indico - DESY, Ettal, Germany|
Duration: 25 Apr 2022 → 30 Apr 2022
Conference number: LL2022
|Conference||16th DESY Workshop on Elementary Particle Physics: Loops and Legs in Quantum Field Theory 2022|
|Period||25/04/22 → 30/04/22|