Color confinement and restoration of residual local gauge symmetries

TL;DR

This paper explores the connection between different gauge fixing conditions and color confinement, showing that topological configurations restore residual gauge symmetry and unify the confinement picture across gauges.

Contribution

It generalizes the color confinement criterion to include topological configurations, bridging the Kugo-Ojima and dual superconductor confinement mechanisms.

Findings

Residual gauge symmetry restoration occurs in Maximal Abelian gauge with topological configurations.

Color confinement is a disordered phase caused by topological configurations, independent of gauge choice.

Compact U(1) gauge theory can exhibit confinement, unlike non-compact U(1).

Abstract

All colored particles including dynamical quarks and gluons are confined if the color confinement criterion proposed by Kugo and Ojima is satisfied. The criterion was obtained under the gauge fixing of the Lorenz type. However, it was pointed out that the Kugo-Ojima criterion breaks down for the Maximal Abelian gauge, which is quite strange in view of the fact that quark confinement has been verified according to the dual superconductivity caused by magnetic monopole condensations. In order to make a bridge between color confinement due to Kugo and Ojima and the dual superconductor picture for quark confinement, we investigate a generalization of the color confinement criterion to obtain the unified picture for confinement. We show that the restoration of the residual local gauge symmetry which was shown in the Lorenz gauge by Hata to be equivalent to the Kugo-Ojima criterion indeed occurs in the Maximal Abelian gauge for the SU(N) Yang-Mills theory in two-, three- and four-dimensional Euclidean spacetime once the singular topological configurations of gauge fields are taken into account. This result indicates that the color confinement phase is a disordered phase caused by non-trivial topological configurations irrespective of the gauge choice. As a byproduct, we show that the compact U(1) gauge theory can have the disordered confinement phase, while the non-compact U(1) gauge theory has the deconfined Coulomb phase.