Dual graph polynomials and a 4-face formula

Doryn, Dmitry

doi:10.4310/ATMP.2018.v22.n2.a3

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Dual graph polynomials and a 4-face formula

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Doryn, Dmitry
Max Planck Institute for Mathematics, Max Planck Society;

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http://dx.doi.org/10.4310/ATMP.2018.v22.n2.a3
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arXiv:1508.03484.pdf
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Citation

Doryn, D. (2018). Dual graph polynomials and a 4-face formula. Advances in Theoretical and Mathematical Physics, 22(2), 395-427. doi:10.4310/ATMP.2018.v22.n2.a3.

Cite as: https://hdl.handle.net/21.11116/0000-0003-AA8D-F

Abstract

We study the dual graph polynomials 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.