Loop-tree duality for integrals on the moduli space of graphs

Connection link: https://hu-berlin.zoom.us/j/61686623112 [4]
Contact: Gaetan Borot (gaetan.borot@hu-berlin.de)

Loop-tree duality is a method for (numerical) computation of momentum space Feynman integrals. In this talk I will present a variant for Feynman integrals in the parametric representation. It is based on a geometrical decomposition of the integration locus, subject to the combinatorics of the Feynman graph under consideration. Since this procedure does not depend on the specific form of the integrand, it also applies to similar integrals, for instance integrals of Francis Brown's canonical forms on the moduli space of graphs. This space is a geometric incarnation of Kontsevich's commutative graph complex, and canonical forms can be used to study its homology. Moreover, it contains a subcomplex, called its spine, which is a classifying space for the outer automorphism group of a free group. In this setting, loop-tree duality arises as integration along the fibers of a map from the moduli space of graphs onto its spine. I will discuss how this can be used to construct forms on the spine, by pushing-forward the above mentioned canonical forms.