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

### Submission summary

 Authors (as Contributors): Kei-Ichi Kondo
Submission information
Date accepted: 2022-05-04
Date submitted: 2022-01-27 03:13
Submitted by: Kondo, Kei-Ichi
Submitted to: SciPost Physics Proceedings
Proceedings issue: XXXIII International Workshop on High Energy Physics (Hard Problems of Hadron Physics: Non-Perturbative QCD & Related Quests)
Ontological classification
Specialties:
• High-Energy Physics - Theory
Approach: Theoretical

### 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.

Published as SciPost Phys. Proc. 6, 013 (2022)

### Submission & Refereeing History

Submission scipost_202201_00037v1 on 27 January 2022

## Reports on this Submission

### Anonymous Report 1 on 2022-3-27 (Invited Report)

• Cite as: Anonymous, Report on arXiv:scipost_202201_00037v1, delivered 2022-03-27, doi: 10.21468/SciPost.Report.4785

### Strengths

1. Very important problem is addressed
2. MA gauge is considered which is a popular gauge for the confinement studies.
3. Nice presentation.

### Report

The authors addressed the famous Kugo-Ogima criterion of color confinement. KO criterion was formulated for the Landau gauge. In the present paper it was demonstrated that the criterion is also valid for the MA gauge. The restoration of the residual local gauge symmetry was used as a method. I recommend the paper for publication after some misprints are corrected.

### Requested changes

1) In the rhs of eq.(12) one of indices $\mu$ should be changed to $\nu$
2) Section 4. It is not clear why two different notations $\phi$ and $\psi$ are used for the matter field.

• validity: high
• significance: high
• originality: top
• clarity: high
• formatting: excellent
• grammar: good