SU(2) Charges with Spherical Symmetry and Confining Boundary Conditions

TL;DR

This paper explores how confining boundary conditions in SU(2) gauge theories imply the existence of topologically charged domain walls, which are crucial for understanding confinement and hadronic dynamics.

Contribution

It demonstrates that confinement involves topologically-charged domain walls in SU(2) gauge theories, linking topological structures to hadronic phenomena.

Findings

Confinement likely involves topologically-charged domain walls.

Surface volume of SU(2) charges resembles a topological insulator.

Classical solutions suggest a mass gap in quantum systems.

Abstract

Applying the static Yang-Mills Maxwell equations to a simple system of SU(2) charges with spherical symmetry and confining boundary conditions provides for a demonstration of the likelihood that the confinement mechanism in non-Abelian gauge theories necessarily involves a topologically-charged domain wall consisting of a surface volume with CP-odd field strength density. The surface volume of a color-singlet system of SU(2) charges therefor describes the magnetic dual of a topological insulator. This essential topological structure in inextricably connected to the hadronic dynamics of the pion tornado. In analogy to the kink solution in the 1+1 dimensional Abelian Higgs model the classical solutions for the field equations in spherically symmetric SU(2) with this domain wall of topological charge can lead to a mass gap in the quantum system