Resummation in QFT with Meijer G-functions

TL;DR

This paper introduces a resummation method using Meijer G-functions to access non-perturbative regimes in quantum field theories, providing new insights into the $eta$-functions and phase structures of various models.

Contribution

It applies a novel resummation technique based on Meijer G-functions to quantum field theories, enabling estimation of non-perturbative effects from limited perturbative data.

Findings

Successfully estimates non-perturbative $eta$-function in $
$ model.

Reproduces instantonic effects using the resummation method.

Uncovers a rich phase diagram in gauge-fermion theories with varying fermion flavors.

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 $\phi^4$ 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.