Renormalization Group Approach to Confinement

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1. Verfasser: Schierholz, Gerrit
Format: Preprint
Veröffentlicht: 2025
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author Schierholz, Gerrit
author_facet Schierholz, Gerrit
contents While we have several complementary models of confinement, some of which are phenomenologically appealing, we do not have the ability to calculate analytically even simple aspects of confinement, let alone have a framework to eventually prove confinement. The problem we are facing is to evolve the theory from the perturbative regime to the long distance confining regime. This is generally achieved by renormalization group transformations. With the gradient flow we now have a technique to address the problem from first principles. The primary focus is on the running coupling $α_S(μ)$, from which confinement can be concluded alone. A central point is that the gluon condensate is scale invariant, which reflects its self-similar behavior across different scales. Building on that, we derive $α_S(μ) \simeq Λ_S^2/μ^2$, which evolves to the infrared fixed point $1/α_S = 0$ in accordance with infrared slavery. The only important factor appears to be the presence of the gluon condensate, which is a universal feature that QCD shares with many other models. The analytical results are supported by numerical simulations.
format Preprint
id arxiv_https___arxiv_org_abs_2509_10658
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Renormalization Group Approach to Confinement
Schierholz, Gerrit
High Energy Physics - Lattice
High Energy Physics - Phenomenology
High Energy Physics - Theory
Nuclear Theory
While we have several complementary models of confinement, some of which are phenomenologically appealing, we do not have the ability to calculate analytically even simple aspects of confinement, let alone have a framework to eventually prove confinement. The problem we are facing is to evolve the theory from the perturbative regime to the long distance confining regime. This is generally achieved by renormalization group transformations. With the gradient flow we now have a technique to address the problem from first principles. The primary focus is on the running coupling $α_S(μ)$, from which confinement can be concluded alone. A central point is that the gluon condensate is scale invariant, which reflects its self-similar behavior across different scales. Building on that, we derive $α_S(μ) \simeq Λ_S^2/μ^2$, which evolves to the infrared fixed point $1/α_S = 0$ in accordance with infrared slavery. The only important factor appears to be the presence of the gluon condensate, which is a universal feature that QCD shares with many other models. The analytical results are supported by numerical simulations.
title Renormalization Group Approach to Confinement
topic High Energy Physics - Lattice
High Energy Physics - Phenomenology
High Energy Physics - Theory
Nuclear Theory
url https://arxiv.org/abs/2509.10658