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On Motives Associated to Graph Polynomials

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arxiv math/0510011 v1 pith:QMPK5IRS submitted 2005-10-01 math.AG hep-th

Spencer Bloch , Hélène Esnault , Dirk Kreimer This is my paper · ORCID
classification math.AGhep-th
keywords functionsfieldaboveanomalousappearanceassociatedattentionbeta
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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.

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Cited by 2 Pith papers

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  1. The motivic Lie algebra embeds into the cohomology of the general linear group

    math.AG 2026-07 conditional novelty 7.0 of 10

    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...

  2. Fano and Reflexive Polytopes from Feynman Integrals

    hep-th 2025-12 unverdicted novelty 6.0 of 10

    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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