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Main Authors: Fukushima, Naoki, Kondo, Kei-Ichi
Format: Preprint
Published: 2025
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Online Access:https://arxiv.org/abs/2507.11101
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author Fukushima, Naoki
Kondo, Kei-Ichi
author_facet Fukushima, Naoki
Kondo, Kei-Ichi
contents We examine the restoration of the residual gauge symmetry in the Yang-Mills theory to be regarded as a confinement criterion. For this purpose we restrict the four-dimensional $SU(2)$ Yang-Mills instantons to those with spatial spherical symmetry $SO(3)$, which automatically causes the dimensional reduction of the four-dimensional $SU(2)$ Yang-Mills theory to the two-dimensional $U(1)$ gauge-scalar theory as implemented explicitly by the Witten transformation. In this setting, we show that the restoration of the residual gauge symmetry occurs due to condensations of instantons and anti-instantons, although the residual gauge symmetry was spontaneously broken in the perturbative vacuum. This result demonstrates that the true confinement phase is a disordered phase in which all internal electric symmetries of the gauge field remain unbroken.
format Preprint
id arxiv_https___arxiv_org_abs_2507_11101
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Residual gauge symmetry and color confinement in the Yang-Mills theory
Fukushima, Naoki
Kondo, Kei-Ichi
High Energy Physics - Theory
We examine the restoration of the residual gauge symmetry in the Yang-Mills theory to be regarded as a confinement criterion. For this purpose we restrict the four-dimensional $SU(2)$ Yang-Mills instantons to those with spatial spherical symmetry $SO(3)$, which automatically causes the dimensional reduction of the four-dimensional $SU(2)$ Yang-Mills theory to the two-dimensional $U(1)$ gauge-scalar theory as implemented explicitly by the Witten transformation. In this setting, we show that the restoration of the residual gauge symmetry occurs due to condensations of instantons and anti-instantons, although the residual gauge symmetry was spontaneously broken in the perturbative vacuum. This result demonstrates that the true confinement phase is a disordered phase in which all internal electric symmetries of the gauge field remain unbroken.
title Residual gauge symmetry and color confinement in the Yang-Mills theory
topic High Energy Physics - Theory
url https://arxiv.org/abs/2507.11101