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arXiv · 1603.04289

The Galois coaction on $\phi^4$ periods

Erik Panzer·Oliver Schnetz
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Abstract

We report on calculations of Feynman periods of primitive log-divergent $\phi^4$ graphs up to eleven loops. The structure of $\phi^4$ periods is described by a series of conjectures. In particular, we discuss the possibility that $\phi^4$ periods are a comodule under the Galois coaction. Finally, we compare the results with the periods of primitive log-divergent non-$\phi^4$ graphs up to eight loops and find remarkable differences to $\phi^4$ periods. Explicit results for all periods we could compute are provided in ancillary files.

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Erik Panzer, Oliver Schnetz. 2016-03-14. The Galois coaction on $\phi^4$ periods. https://doi.org/10.4310/cntp.2017.v11.n3.a3

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