The Galois coaction on ${\varphi }^4$ periods

Abstract

We report on calculations of Feynman periods of primitive log-divergent ${\varphi }^4$ graphs up to eleven loops. The structure of ${\varphi }^4$ periods is described by a series of conjectures. In particular, we discuss the possibility that ${\varphi }^4$ periods are a comodule under the Galois coaction. Finally, we compare the results with the periods of primitive log-divergent non-${\varphi }^4$ graphs up to eight loops and find remarkable differences to ${\varphi }^4$ periods. Explicit results for all periods we could compute are provided in ancillary files.

extensive data sets for phi^4 periods up to 11 loops (complete up to 7 loops) and non-phi^4 periods up to 8 loops are attached as ancillary files; v2: several clarifications and examples added

References in corpus (5)

• Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integrals
• Framings for graph hypersurfaces
• On the decomposition of motivic multiple zeta values
• Galois theory, motives and transcendental numbers
• Multiple Deligne values: a data mine with empirically tamed denominators

Cited by in corpus (36)

• Minimally subtracted six loop renormalization of $O(n)$-symmetric ${\varphi }^4$ theory and critical exponents
• Numbers and Functions in Quantum Field Theory
• The two-loop five-point amplitude in $\mathcal{N}=4$ super-Yang-Mills theory
• Six-Gluon Amplitudes in Planar $\mathcal{N}=4$ Super-Yang-Mills Theory at Six and Seven Loops
• A (Bounded) Bestiary of Feynman Integral Calabi-Yau Geometries
• The Cosmic Galois Group and Extended Steinmann Relations for Planar $\mathcal{N}=4$ SYM Amplitudes
• Analytic Structure of all Loop Banana Amplitudes
• Diagrammatic Hopf algebra of cut Feynman integrals: the one-loop case
• Five loop renormalization of ${\varphi }^3$ theory with applications to the Lee-Yang edge singularity and percolation theory
• The critical O(N) CFT: Methods and conformal data
• Embedding Feynman Integral (Calabi-Yau) Geometries in Weighted Projective Space
• Duals of Feynman Integrals, I: Differential Equations
• The Double Pentaladder Integral to All Orders
• A Three-Point Form Factor Through Five Loops
• The Origin of the Six-Gluon Amplitude in Planar $\mathcal{N}=4$ SYM
• The SAGEX Review on Scattering Amplitudes, Chapter 3: Mathematical structures in Feynman integrals
• Bootstrapping a Stress-Tensor Form Factor through Eight Loops
• Lifting Heptagon Symbols to Functions
• From positive geometries to a coaction on hypergeometric functions
• Two-loop diagrams in non-relativistic QCD with elliptics
• Integrated correlators in $\mathcal{N}=4$ super Yang-Mills and periods
• Coaction and double-copy properties of configuration-space integrals at genus zero
• Glue-and-Cut at Five Loops
• Recursive computation of Feynman periods
• Lambert-W solves the noncommutative ${\Phi }^4$-model
• Transcendental structure of multiloop massless correlators and anomalous dimensions
• Cosmic Wheels: From integrability to the Galois coaction
• Instantons or Renormalons? A Comment on phi4_4 Theory in the MS Scheme
• Non-planar integrated correlator in $\mathcal{N}=4$ SYM
• Notes on conformal integrals: Coulomb branch amplitudes, magic identities and bootstrap
• An Introduction to Motivic Feynman Integrals
• Statistics of Feynman amplitudes in ${\varphi }^4$-theory
• Relativistic causality and position space renormalization
• Anomalous dimensions at small spins
• Unstable cohomology of ${\mathsf{GL}}_{2n}(\mathbb{Z})$ and the odd commutative graph complex
• Hyperlogarithms and periods in Feynman amplitudes