Recursive computation of Feynman periods

Abstract

Feynman periods are Feynman integrals that do not depend on external kinematics. Their computation, which is necessary for many applications of quantum field theory, is greatly facilitated by graphical functions or the equivalent conformal four-point integrals. We describe a set of transformation rules that act on such functions and allow their recursive computation in arbitrary even dimensions. As a concrete example we compute all subdivergence-free Feynman periods in ${\varphi }^3$ theory up to six loops and 561 of 607 Feynman periods at seven loops. Our results support the conjectured existence of a coaction structure in quantum field theory and suggest that ${\varphi }^3$ and ${\varphi }^4$ theory share the same number content.

arXiv comment45 pages + long appendix with 700+ Feynman graphs; a list of phi^3 periods up to 9 loops is attached as ancillary file; v2: historical remarks added, accepted version to appear in JHEP

References in corpus (35)

• Direct Proof Of Tree-Level Recursion Relation In Yang-Mills Theory
• Differential Equations for Feynman Graph Amplitudes
• Renormalization in quantum field theory and the Riemann-Hilbert problem I: the Hopf algebra structure of graphs and the main theorem
• Magic identities for conformal four-point integrals
• Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integrals
• Minimally subtracted six loop renormalization of $O(n)$-symmetric ${\varphi }^4$ theory and critical exponents
• The massless higher-loop two-point function
• Four Loop Massless Propagators: an Algebraic Evaluation of All Master Integrals
• On Motives Associated to Graph Polynomials
• Numbers and Functions in Quantum Field Theory
• Leading singularities and off-shell conformal integrals
• Master Integrals for Four-Loop Massless Propagators up to Transcendentality Weight Twelve
• Knots and Numbers in ${\varphi }^4$ Theory to 7 Loops and Beyond
• A K3 in phi4
• Traintracks Through Calabi-Yaus: Amplitudes Beyond Elliptic Polylogarithms
• Gluing Ladders into Fishnets
• Analytic Structure of all Loop Banana Amplitudes
• Five loop renormalization of ${\varphi }^3$ theory with applications to the Lee-Yang edge singularity and percolation theory
• Multi-loop Feynman integrals and conformal quantum mechanics
• Tropical curves, graph complexes, and top weight cohomology of M_g
• The Galois coaction on ${\varphi }^4$ periods
• Unknotting the polarized vacuum of quenched QED
• Yangian Bootstrap for Conformal Feynman Integrals
• Tropical Monte Carlo quadrature for Feynman integrals
• On the status of expansion by regions
• Feynman graph generation and calculations in the Hopf algebra of Feynman graphs
• Renormalized asymptotic enumeration of Feynman diagrams
• Resonant resurgent asymptotics from quantum field theory
• Graphical functions in parametric space
• Glue-and-Cut at Five Loops
• The Hopf algebra structure of the $R^{\ast }$-operation
• Yangian Ward Identities for Fishnet Four-Point Integrals
• Instantons or Renormalons? A Comment on phi4_4 Theory in the MS Scheme
• Bootstrapping 2d ${\varphi }^4$ Theory with Hamiltonian Truncation Data
• Conformal Triangles and Zig-Zag Diagrams

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• Resonant resurgent asymptotics from quantum field theory
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