Residual gauge symmetry and color confinement in the Yang-Mills theory

Naoki Fukushima; Kei-Ichi Kondo

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arXiv · 2507.11101

Residual gauge symmetry and color confinement in the Yang-Mills theory

Naoki Fukushima·Kei-Ichi Kondo

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Abstract

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.

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Naoki Fukushima, Kei-Ichi Kondo. 2025-07-15. Residual gauge symmetry and color confinement in the Yang-Mills theory. https://arxiv.org/abs/2507.11101

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