Confinement, mass gap and gauge symmetry in the Yang-Mills theory -- restoration of residual local gauge symmetry

TL;DR

This paper proposes a universal confinement criterion based on residual gauge symmetry restoration, applicable to various gauge theories and gauges, linking topological configurations to confinement phases.

Contribution

It introduces a new confinement criterion based on residual gauge symmetry restoration, applicable across different gauges and formulations, unifying understanding of confinement.

Findings

Restoration of residual gauge symmetry occurs in Maximal Abelian gauge for SU(N) Yang-Mills.

Confinement phase is associated with topological configurations causing disorder.

Criterion applies to both Abelian and non-Abelian gauge theories, compact or non-compact.

Abstract

In this talk we want to discuss the color confinement criterion which guarantees confinement of all colored particles including dynamical quarks and gluons. The most well-known criterion is the Kugo-Ojima color confinement criterion derived in the Lorenz gauge. However, it was pointed out that the Kugo-Ojima criterion breaks down for the Maximal Abelian gauge in which quark confinement has been verified according to the dual superconductivity caused by magnetic monopole condensations. We give the color confinement criterion based on the restoration of the residual local gauge symmetry which can be applied to the Abelian and non-Abelian gauge theories as well irrespective of the compact or non-compact formulation, and enables us to understand confinement in all the cases. Indeed, the restoration of the residual local gauge symmetry which was shown by Hata in the Lorenz gauge 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.