Framings for graph hypersurfaces

Understand

We present a method for computing the framing on the cohomology of graph hypersurfaces defined by the Feynman differential form.

• This answers a question of Bloch, Esnault and Kreimer in the affirmative for an infinite class of graphs for which the framings are Tate motives.
• Applying this method to the modular graphs of Brown and Schnetz, we find that the Feynman differential form is not of Tate type in general.
• This finally disproves a folklore conjecture stating that the periods of Feynman integrals of primitive graphs in phi^4 theory factorise through a category of mixed Tate motives.