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Research PaperNo Access

Resurgence and self-completion in renormalized gauge theories

Alessio Maiezza

https://orcid.org/0000-0001-8938-9400

Dipartimento di Scienze Fisiche e Chimiche, Università degli Studi dell’Aquila, via Vetoio, L’Aquila I-67100, Italy

E-mail Address: alessiomaiezza@gmail.com

Corresponding author.

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and

Juan Carlos Vasquez

https://orcid.org/0000-0001-5940-4059

Department of Physics and Astronomy, Amherst College, Amherst, MA 01002, USA

E-mail Address: jvasquezcarmona@amherst.edu

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https://doi.org/10.1142/S0217751X24500258Cited by:2 (Source: Crossref)

Abstract

Under certain assumptions and independent of the instantons, we show that the logarithm expansion of dimensional regularization in quantum field theory needs a nonperturbative completion to have a renormalization group flow valid at all energies. Then, we show that such nonperturbative completion has the analytic properties of the renormalons, which we find with only a marginal reference to diagrammatic calculations. We demonstrate that renormalon corrections necessarily lead to analyzable functions, namely, resurgent transseries. A detailed analysis of the resurgent properties of the renormalons is provided. The self-consistency of the theory requires these nonperturbative contributions to render the running coupling well defined at any energy, thus with no Landau pole. We illustrate the point within the case of quantum electrodynamics (QED). This way, we explicitly realize the correspondence between the nonperturbative Landau pole scale and the renormalons. What is seen as a Landau pole in perturbation theory is cured by the nonperturbative, resurgent contributions.

Keywords:

PACS: 03.70.+k, 03.65.Ca, 02.30.Hq

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Vol. 39, No. 05n06

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History

Received 18 January 2024

Revised 26 February 2024

Accepted 28 February 2024

Published: 4 April 2024

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