Landau-Khalatnikov-Fradkin transformation and the mystery of even $\zeta$-values in Euclidean massless correlators

Abstract

The Landau-Khalatnikov-Fradkin (LKF) transformation is a powerful and elegant transformation allowing to study the gauge dependence of the propagator of charged particles interacting with gauge fields. With the help of this transformation, we derive a non-perturbative identity between massless propagators in two different gauges. From this identity, we find that the corresponding perturbative series can be exactly expressed in terms of a hatted transcendental basis that eliminates all even Euler $\zeta$-functions. This explains the mystery of even $\zeta$-values observed in multi-loop calculations of Euclidean massless correlators for almost three decades now. Our construction further allows us to derive an exact formula relating hatted and standard $\zeta$-functions to all orders of perturbation theory.

(v2) 9 pages, no figure, published in PRD, few edits in text (some per referee's comments) and references added, no change in results. (v1) 9 pages, no figure

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Cited by in corpus (13)

• Abelian Higgs model at four loops, fixed-point collision and deconfined criticality
• Scattering amplitudes in the Regge limit and the soft anomalous dimension through four loops
• Glue-and-Cut at Five Loops
• Landau-Khalatnikov-Fradkin transformation of the fermion propagator in massless reduced QED
• Landau-Khalatnikov-Fradkin transformation in three-dimensional quenched QED
• Landau-Khalatnikov-Fradkin Transformations, Nielsen Identities, Their Equivalence and Implications for QCD
• The Generalised LKF Transformations for Arbitrary $N$-point Fermion Correlators
• Four-loop singularities of the massless fermion propagator in quenched three-dimensional QED
• Non-perturbative field theoretical aspects of graphene and related systems
• Landau-Khalatnikov-Fradkin transformations for the two loop massless quark propagator
• Correlators of vector, tensor, and scalar composite vertices of order $O({\alpha }_s^2{\beta }_0)$
• Landau-Khalatnikov-Fradkin transformation and hatted zeta-values
• Landau-Khalatnikov-Fradkin Transformation and Even zeta Functions