Abstract:

A convenient integral representation for zig-zag four-point and two-point planar Feynman diagrams relevant to the bi-scalar D-dimensional fishnet field theory is obtained. This representation gives a possibility to evaluate exactly diagrams of the zig-zag series in special cases. I recall a very interesting history of the problem and give a fairly simple proof of the Broadhurst-Kreimer conjecture about the values of zig-zag diagrams which make a significant contribution to the renormalization group β-function in 4-dimensional φ⁴ theory.