Wick rotations, Eichler integrals, and multi-loop Feynman diagrams

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 $L$-series, and verify several recent conjectures of Broadhurst.

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

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