On the periods of some Feynman integrals

Abstract

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

References in corpus (3)

• A K3 in phi4
• Parametric Representation of Noncommutative Field Theory
• Quantum field theory over F_q

Cited by in corpus (66)

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• Proof of the zig-zag conjecture
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• Framings for graph hypersurfaces
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• Algebraic Structures in local QFT
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