Dual graph polynomials and a $4$-face formula

We study the dual graph polynomials $\varphi_G$ 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.

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Published 3 October 2018