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

摘要

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.