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On Motives Associated to Graph Polynomials
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abstract
The appearance of multiple zeta values in anomalous dimensions and $\beta$-functions of renormalizable quantum field theories has given evidence towards a motivic interpretation of these renormalization group functions. In this paper we start to hunt the motive, restricting our attention to a subclass of graphs in four dimensional scalar field theory which give scheme independent contributions to the above functions.
Forward citations
Cited by 4 Pith papers
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Hepp's bound for Feynman graphs and matroids
The Hepp bound, a rational matroid invariant from tropicalizing the Feynman period integral, provably respects all known graph period symmetries and correlates strongly with actual periods.
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The motivic Lie algebra embeds into the cohomology of the general linear group
The motivic Lie algebra of mixed Tate motives over Z is shown to embed canonically into unstable compactly-supported cohomology of GL_g(Z)-locally symmetric spaces and of A_g, via canonical graph cocycles that are gen...
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Graph theoretic properties of Speyer's matroid polynomial $g_M(t)$
For graphic and cographic matroids, the derivative g'_M(-1) equals (-1)^{c(M)-1} c(M), and computational data suggests many new properties of the coefficient N2.
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Fano and Reflexive Polytopes from Feynman Integrals
Quasi-finite Feynman integrals produce sparse Fano and reflexive polytopes that encode degenerate Calabi-Yau varieties and link to del Pezzo surfaces, K3 surfaces, and Calabi-Yau threefolds.
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