Resummation in QFT with Meijer G-functions

Abstract

We employ a recent resummation method to deal with divergent series, based on the Meijer G-function, which gives access to the non-perturbative regime of any QFT from the first few known coefficients in the perturbative expansion. Using this technique, we consider in detail the ${\varphi }^4$ model where we estimate the non-perturbative $\beta -$function and prove that its asymptotic behavior correctly reproduces instantonic effects calculated using semiclassical methods. After reviewing the emergence of the renormalons in this theory, we also speculate on how one can resum them. Finally, we resum the non-perturbative $\beta -$function of abelian and non-abelian gauge-fermion theories and analyze the behavior of these theories as a function of the number of fermion flavors. While in the former no fixed points are found, in the latter, a richer phase diagram is uncovered and illustrated by the regions of confinement, large-distance conformality, and asymptotic safety.

22 pages, 10 figures, final version with minor changes, as accepted in NPB

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• Resonant resurgent asymptotics from quantum field theory
• Hidden Conformal Symmetry from the Lattice
• Non-local Lagrangians from Renormalons and Analyzable Functions
• Looking through the QCD Conformal Window with Perturbation Theory
• Weak-Coupling, Strong-Coupling and Large-Order Parametrization of the Hypergeometric-Meijer Approximants
• Non-Wilsonian ultraviolet completion via transseries
• Spectral Functions of Gauge Theories with Banks-Zaks Fixed Points
• Addressing energy density functionals in the language of path-integrals I: Comparative study of diagrammatic techniques applied to the (0+0)-D $O(N)$-symmetric ${\phi }^4$-theory
• Weather Forecast for Vacuum Fluctuations in QED