Kinematic singularities of Feynman integrals and principal A-determinants

Abstract

We consider the analytic properties of Feynman integrals from the perspective of general A-discriminants and A-hypergeometric functions introduced by Gelfand,Kapranov and Zelevinsky (GKZ). This enables us, to give a clear and mathematically rigour description of the singular locus, also known as Landau variety, via principal A-determinants. We also comprise a description of the various second type singularities. Moreover, by the Horn-Kapranov-parametrization we give a very efficient way to calculate a parametrization of Landau varieties. We furthermore present a new approach to study the sheet structure of multivalued Feynman integrals by use of coamoebas.

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• Macaulay Matrix for Feynman Integrals: Linear Relations and Intersection Numbers
• Landau Singularities Revisited: Computational Algebraic Geometry for Feynman Integrals
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• What is the $i\epsilon$ for the S-matrix?
• Principal Landau Determinants
• Symbol Alphabets from the Landau Singular Locus
• Constraints on Sequential Discontinuities from the Geometry of On-shell Spaces
• Generalized Cuts of Feynman Integrals in Parameter Space
• Analytic continuations and numerical evaluation of the Appell $F_1$, $F_3$, Lauricella $F_D^{(3)}$ and Lauricella-Saran $F_S^{(3)}$ and their Application to Feynman Integrals
• On Feynman graphs, matroids, and GKZ-systems
• GKZ hypergeometric systems of the three-loop vacuum Feynman integrals
• GKZ hypergeometric systems of the four-loop vacuum Feynman integrals