Communications in Number Theory and Physics
Volume 11 (2017)
The Galois coaction on $\phi^4$ periods
Pages: 657 – 705
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.
Paper received on 18 March 2016.
Paper accepted on 23 August 2016.