Abstract / Description of output
We study the algebraic and analytic structure of Feynman integrals by proposing an operation that maps an integral into pairs of integrals obtained from a master integrand and a corresponding master contour. This operation is a coaction. It reduces to the known coaction on multiple polylogarithms, but applies more generally, e.g., to hypergeometric functions. The coaction also applies to generic oneloop Feynman integrals with any configuration of internal and external masses, and in dimensional regularization. In this case, we demonstrate that it can be given a diagrammatic representation 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 facilitates a straightforward derivation of the differential equations they admit. In particular, the differential equations for any oneloop integral are determined by the diagrammatic coaction using limited information about their maximal, nexttomaximal, and nexttonexttomaximal cuts.
Original language  English 

Article number  051601 
Journal  Physical Review Letters 
Volume  119 
Early online date  31 Jul 2017 
DOIs  
Publication status  Published  4 Aug 2017 
Keywords / Materials (for Nontextual outputs)
 hepth
 hepph
 mathph
 math.MP
 math.NT
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Einan Gardi
 School of Physics and Astronomy  Personal Chair of Theoretical Physics
Person: Academic: Research Active