Abstract
We obtain a convenient representation for a series of two-point and four-point diagrams related to the \(D\)-dimensional fishnet field theory. This representation allows one to obtain an exact expression for the zig-zag series diagrams in the \({{\phi }^{4}}\) field theory, which leads to a relatively simple proof of the zig-zag conjecture formulated by D. Broadhurst and D. Kreimer.
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This work was supported by the Basis Theoretical Physics and Mathematics Advancement Foundation. The work of L.A. Shumilov was supported by the Ministry of Science and Higher Education of the Russian Federation, agreement no. 075-15-2022-289.
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Derkachev, S.E., Isaev, A.I. & Shumilov, L.A. Zig-Zag Diagrams and Conformal Triangles. Phys. Part. Nuclei Lett. 20, 240–245 (2023). https://doi.org/10.1134/S1547477123030214
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DOI: https://doi.org/10.1134/S1547477123030214