Feynman motives of banana graphs

Details Feynman motives of banana graphs Feynman motives of banana graphs

2008-07-10

arxiv.org/abs/0807.1690v2

Commun. Number Theory Phys. 3 (2009), no. 1, 1-57

Physics

High Energy Physics

High Energy Physics - Theory

35 pages, LaTeX, 9 eps figures (v2: small corrections)

Scientific paper

We consider the infinite family of Feynman graphs known as the "banana graphs" and compute explicitly the classes of the corresponding graph hypersurfaces in the Grothendieck ring of varieties as well as their Chern-Schwartz-MacPherson classes, using the classical Cremona transformation and the dual graph, and a blowup formula for characteristic classes. We outline the interesting similarities between these operations and we give formulae for cones obtained by simple operations on graphs. We formulate a positivity conjecture for characteristic classes of graph hypersurfaces and discuss briefly the effect of passing to noncommutative spacetime.

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