Color structure of quantum SU(N) Yang-Mills theory

TL;DR

This paper explores the color structure in quantum SU(N) Yang-Mills theories, proposing that Weyl symmetry uniquely determines color attributes and suggesting confinement is specific to SU(3) based on classical solutions.

Contribution

It introduces a Weyl symmetric ansatz for classical solutions in SU(3) Yang-Mills theory, linking Weyl symmetry to color confinement and vacuum structure, and extends the analysis to SU(N).

Findings

Weyl symmetry governs all color attributes of quantum states.

Classical solutions describe color singlet states for gluons and quarks.

Color confinement is specific to SU(3) Yang-Mills theory.

Abstract

Color confinement is the most puzzling phenomenon in the theory of strong interaction based on a quantum SU(3) Yang-Mills theory. The origin of color confinement supposed to be intimately related to non-perturbative features of the non-Abelian gauge theory, and touches very foundations of the theory. We revise basic concepts underlying QCD concentrating mainly on concepts of gluons and quarks and color structure of quantum states. Our main idea is that a Weyl symmetry is the only color symmetry which determines all color attributes of quantum states and physical observables. We construct an ansatz for classical Weyl symmetric dynamical solutions in SU(3) Yang-Mills theory which describe one particle color singlet quantum states for gluons and quarks. Abelian Weyl symmetric solutions provide microscopic structure of a color invariant vacuum and vacuum gluon condensates. This resolves a problem of existence of a gauge invariant and stable vacuum in QCD. Generalization of our consideration to SU(N) (N=4,5) Yang-Mills theory implies that the color confinement phase is possible only in SU(3) Yang-Mills theory.