Advances in Theoretical and Mathematical Physics

Volume 21 (2017)

Number 8

The $c_2$ invariant is invariant

Pages: 1953 – 1989

DOI: http://dx.doi.org/10.4310/ATMP.2017.v21.n8.a3

Author

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

Abstract

The $c_2$ invariants in all $4$ different representations of the Feynman period (parametric and dual parametric representations, position and momentum spaces) coincide for all log-divergent graphs that satisfy the condition called duality admissibility. We check this condition for a good subspace of graphs with certain combinatorial properties, for instance, for all planar graphs. After the result in “Dual graph polynomials and a $4$-face formula” [D. Doryn, arXiv:1508.03484], the coincidence holds for all physically relevant graphs.

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Published 29 March 2018