# 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.

## Key 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

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Source: https://tomesphere.com/paper/1905.01529