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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.11101 |
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| _version_ | 1866918176832356352 |
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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 |