Wick rotations, Eichler integrals, and multi-loop Feynman diagrams
Number Theory
2018-05-01 v4 High Energy Physics - Theory
Algebraic Geometry
Abstract
Using contour deformations and integrations over modular forms, we compute certain Bessel moments arising from diagrammatic expansions in two-dimensional quantum field theory. We evaluate these Feynman integrals as either explicit constants or critical values of modular -series, and verify several recent conjectures of Broadhurst.
Cite
@article{arxiv.1706.08308,
title = {Wick rotations, Eichler integrals, and multi-loop Feynman diagrams},
author = {Yajun Zhou},
journal= {arXiv preprint arXiv:1706.08308},
year = {2018}
}
Comments
i+37 pages. Simplification and generalization of Bloch-Kerr-Vanhove (arXiv:1406.2664) and Samart (arXiv:1511.07947). Verification of several conjectures by Broadhurst (arXiv:1604.03057) on critical values of modular L-series. Revised according to referees' reports