# On the periods of some Feynman integrals - Mathematics > Algebraic Geometry

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Abstract: We study the related questions: i when Feynman amplitudes in massless$\phi^4$ theory evaluate to multiple zeta values, and ii when theirunderlying motives are mixed Tate. More generally, by consideringconfigurations of singular hypersurfaces which fiber linearly over each other,we deduce sufficient geometric and combinatorial criteria on Feynman graphs forboth i and ii to hold. These criteria hold for some infinite classes ofgraphs which essentially contain all cases previously known to physicists.Calabi-Yau varieties appear at the point where these criteria fail.

Autor: Francis C. S. Brown

Fuente: https://arxiv.org/