Spanning forest polynomials and the transcendental weight of Feynman graphs

Abstract

We give combinatorial criteria for predicting the transcendental weight of Feynman integrals of certain graphs in ${\varphi }^4$ theory. By studying spanning forest polynomials, we obtain operations on graphs which are weight-preserving, and a list of subgraphs which induce a drop in the transcendental weight.

30 pages

Cited by in corpus (17)

• Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integrals
• Lectures on differential equations for Feynman integrals
• A K3 in phi4
• A (Bounded) Bestiary of Feynman Integral Calabi-Yau Geometries
• On hyperlogarithms and Feynman integrals with divergences and many scales
• Prescriptive Unitarity
• Analytic results for planar three-loop four-point integrals from a Knizhnik-Zamolodchikov equation
• Duals of Feynman Integrals, 2: Generalized Unitarity
• Tropical Monte Carlo quadrature for Feynman integrals
• The massless hexagon integral in D = 6 dimensions
• On the analytic computation of massless propagators in dimensional regularization
• Graphical functions in parametric space
• Higher loop corrections to a Schwinger--Dyson equation
• Combinatorial proof of a Non-Renormalization Theorem
• On Solving Dual Conformal Integrals in Coulomb-branch Amplitudes and Their Periods
• On $c_2$ invariants of 4-regular Feynman graphs
• $c_2$ invariants of hourglass chains via quadratic denominator reduction