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Feynman motives of banana graphs

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arxiv 0807.1690 v2 pith:7OEYL56G submitted 2008-07-10 hep-th math-phmath.AGmath.MP

Paolo Aluffi (FSU) , Matilde Marcolli (MPI) This is my paper · ORCID
classification hep-thmath-phmath.AGmath.MP
keywords classesgraphsgraphbananacharacteristicfeynmanhypersurfacesoperations
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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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  1. Special Fano geometry from Feynman integrals

    hep-th 2024-12 conditional novelty 5.0 of 10

    Special Fano varieties, which include Calabi-Yau spaces as the Q=1 case, arise from the Symanzik polynomials of several families of Feynman integrals.

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