c_2 Invariants of Recursive Families of Graphs
Combinatorics
2017-05-23 v2 Mathematical Physics
math.MP
Abstract
The c_2 invariant, defined by Schnetz in 2011, is an arithmetic graph invariant created towards a better understanding of Feynman integrals. This paper looks at some graph families of interest, with a focus on decompleted toroidal grids. Specifically, the c_2 invariant for p=2 is shown to be zero for all decompleted non-skew toroidal grids. We also calculate the c_2 invariant at p=2 for G a family of graphs called X-ladders. Finally, we show these methods can be applied to any graph with a recursive structure, for any fixed p.
Cite
@article{arxiv.1701.01208,
title = {c_2 Invariants of Recursive Families of Graphs},
author = {Wesley Chorney and Karen Yeats},
journal= {arXiv preprint arXiv:1701.01208},
year = {2017}
}
Comments
15 pages, 13 figures. To appear in Annales de L'Institut Henri Poincare D