On Feynman graphs, matroids, and GKZ-systems

Abstract

We show in several important cases that the $A$-hypergeometric system attached to a Feynman diagram in Lee--Pomeransky form, obtained by viewing the momenta and the nonzero masses as indeterminates, has a normal underlying semigroup. This continues a quest initiated by Klausen, and studied by Helmer and Tellander. In the process we identify several relevant matroids related to the situation and explore their relationships.

arXiv comment20 pages

References in corpus (7)

• On Motives Associated to Graph Polynomials
• Feynman integrals as A-hypergeometric functions
• Kinematic singularities of Feynman integrals and principal A-determinants
• Algebraic aspects of hypergeometric differential equations
• Cohen-Macaulay Property of Feynman Integrals
• Matroid connectivity and singularities of configuration hypersurfaces
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Cited by in corpus (5)

• Symbol Alphabets from the Landau Singular Locus
• $D$-Module Techniques for Solving Differential Equations in the Context of Feynman Integrals
• GKZ hypergeometric systems of the three-loop vacuum Feynman integrals
• GKZ hypergeometric systems of the four-loop vacuum Feynman integrals
• Tropical Feynman integration in the physical region