Weyl group, CP and the kink-like field configurations in the effective SU(3) gauge theory

TL;DR

This paper explores the structure of the effective potential in SU(3) gauge theory, revealing degenerate minima connected by symmetry transformations, which lead to kink-like gauge field configurations and implications for the spectrum of scalar fields.

Contribution

It demonstrates the existence of twelve degenerate minima in the effective SU(3) gauge theory and analyzes the resulting kink-like solutions and their physical implications.

Findings

Existence of twelve degenerate minima connected by Weyl and parity transformations.

Kink-like gauge field configurations interpolate between different minima.

Discussion of scalar field spectrum in kink backgrounds.

Abstract

Effective Lagrangian for pure Yang-Mills gauge fields invariant under the standard space-time and local gauge SU(3) transformations is considered. It is demonstrated that a set of twelve degenerated minima exists as soon as a nonzero gluon condensate is postulated. The minima are connected to each other by the parity transformations and Weyl group transformations associated with the color su(3) algebra. The presence of degenerated discrete minima in the effective potential leads to the solutions of the effective Euclidean equations of motion in the form of the kink-like gauge field configurations interpolating between different minima. Spectrum of charged scalar field in the kink background is discussed.