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Vector Spaces of Generalized Euler Integrals

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arxiv 2208.08967 v2 pith:4CT5HLB6 submitted 2022-08-18 math.AG hep-th

Daniele Agostini , Claudia Fevola , Anna-Laura Sattelberger , Simon Telen This is my paper
classification math.AGhep-th
keywords eulerintegralsgeneralizedspacestoolsvectoraffinealgebra
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abstract

We study vector spaces associated to a family of generalized Euler integrals. Their dimension is given by the Euler characteristic of a very affine variety. Motivated by Feynman integrals from particle physics, this has been investigated using tools from homological algebra and the theory of $D$-modules. We present an overview and uncover new relations between these approaches. We also provide new algorithmic tools.

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  1. Differential Space of Feynman Integrals: Annihilators and $\mathcal{D}$-module

    hep-th 2025-06 conditional novelty 6.0 of 10

    A Griffiths-Dwork based algorithm builds annihilators and D-modules for Feynman-like integrals, and in all tested cases the holonomic rank matches the twisted de Rham cohomology dimension.

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