Landau-Khalatnikov-Fradkin transformation and hatted zeta-values

Abstract

We show an exact formula obtained in [1], which relates hatted and standard zeta-values to all orders of perturbation theory. The formula is based on the Landau-Khalatnikov-Fradkin (LKF) transformation between the massless propagators of charged particles interacting with gauge fields, in two different gauges.

arXiv comment8 pages; contribution to the proceedings of International Bogolyubov Conference "Problems of Theoretical and Mathematical Physics" (September 9 - 13, 2019; Dubna, Russia); based on arXiv:1906.10930

References in corpus (27)

• Five-Loop Running of the QCD coupling constant
• The five-loop beta function of Yang-Mills theory with fermions
• NLO corrections to the BFKL equation in QCD and in supersymmetric gauge theories
• Adler Function, Bjorken Sum Rule, and the Crewther Relation to Order alpha_s^4 in a General Gauge Theory
• Four Loop Massless Propagators: an Algebraic Evaluation of All Master Integrals
• Analytic two-loop results for selfenergy- and vertex-type diagrams with one non-zero mass
• Dressing and Wrapping
• The Collinear Limit of the Energy-Energy Correlator
• Four loop twist two, BFKL, wrapping and strings
• Five-Loop Anomalous Dimension of Twist-Two Operators
• Five-loop renormalisation of QCD in covariant gauges
• An Étude in non-linear Dyson--Schwinger Equations
• Five-loop contributions to low-N non-singlet anomalous dimensions in QCD
• Multi-loop techniques for massless Feynman diagram calculations
• Landau-Khalatnikov-Fradkin Transformations and the Fermion Propagator in Quantum Electrodynamics
• Twist-2 at seven loops in planar N=4 SYM theory: Full result and analytic properties
• Absence of pi^2 terms in physical anomalous dimensions in DIS: verification and resulting predictions
• Renormalization group functions for the Wess-Zumino model: up to 200 loops through Hopf algebras
• Landau-Khalatnikov-Fradkin transformations in Reduced Quantum Electrodynamics
• The structure of generic anomalous dimensions and no-$\pi$ theorem for massless propagators
• On DIS Wilson coefficients in N = 4 super Yang-Mills theory
• Landau-Khalatnikov-Fradkin transformation and the mystery of even $\zeta$-values in Euclidean massless correlators
• Konishi OPE coefficient at the five loop order
• A fresh look at the (non-)Abelian Landau-Khalatnikov-Fradkin transformations
• Landau-Khalatnikov-Fradkin transformation for the fermion propagator in QED in arbitrary dimensions
• Transcendental structure of multiloop massless correlators and anomalous dimensions
• Landau-Khalatnikov-Fradkin transformation of the fermion propagator in massless reduced QED

Cited by in corpus (1)

• Four-loop singularities of the massless fermion propagator in quenched three-dimensional QED