Residual gauge symmetry and color confinement in the Yang–Mills theory
Year: 2025
Type: article
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 S U ( 2 ) Yang–Mills instantons to those with spatial spherical symmetry S O ( 3 ) , which automatically causes the dimensional reduction of the four-dimensional S U ( 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.
Source: Nuclear Physics B
Authors: Naoki Fukushima, Kei-Ichi Kondo
Institutions: Chiba University, Keio University
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4415446966