Advances in Theoretical and Mathematical Physics

Volume 22 (2018)

Number 2

Dual graph polynomials and a $4$-face formula

Pages: 395 – 427

DOI: http://dx.doi.org/10.4310/ATMP.2018.v22.n2.a3

Author

Dmitry Doryn (IBS Center for Geometry and Physics, Pohang, Gyeongbuk, Korea)

Abstract

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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