The algebraic structure of cut Feynman integrals and the diagrammatic coaction
  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 one-loop 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 one-loop integral are
determined by the diagrammatic coaction using limited information about their
maximal, next-to-maximal, and next-to-next-to-maximal cuts.
