Dual graph polynomials and a 4-face formula

Abstract

We study the dual graph polynomials phi(G) and the case when a Feynman graph has no triangles but has a 4-face. This leads to the proof of the duality admissibility of all graphs up to 18 loops. As a consequence, the c(2) invariant is the same for all 4 Feynman period representations (position, momentum, parametric and dual parametric) for any physically relevant graph. (c)2018 International press of Boston, Inc