Field-Strength Descriptions for a System of Classical SU(2) Charges with Spherical Symmetry and Confining Boundary Conditions

TL;DR

This paper investigates field-strength solutions for a spherically symmetric SU(2) charge system with confining boundary conditions, revealing types of solutions that model non-Abelian confinement mechanisms relevant to QCD.

Contribution

It introduces a classification of solutions to Yang-Mills equations with confining boundary conditions, including topologically nontrivial states resembling a spherical dual topological insulator.

Findings

Type-0 solutions describe topologically trivial bound states.

Type-1 and type-2 solutions involve domain walls with topological charge.

Both solution types model non-Abelian confinement phenomena.

Abstract

The existence of a mechanism within the non-Abelian dynamics of QCD that confines quarks and gluons to the interior of hadrons has long been accepted empirically. To explore what this mechanism might look like, this paper examines field-strength descriptions for an extended system of SU(2) charges with spherical symmetry and imposes alternate confining boundary conditions to the time-independent Yang-Mills Maxwell equations. Three types of global solutions to the set of equations can be distinguished: types 0,1,and2. Type-0 solutions evade the nonlinear dynamics associated with the radial magnetic field to describe a topologically trivial bound state. Type-1 and type-2 solutions both require a domain wall of topological charge to separate the interior volume containing the SU(2) charge densities from the exterior volume where the boundary conditions are imposed. Type-1 solutions describe an exterior volume with a radial magnetic field while type-2 solutions contain a sterile exterior volume where all field-strengths vanish. These solutions both describe a non-Abelian "spherical dual topological insulator". the dimensional reduction associated with the imposition of spherical system of SU(2) charges can also be applied to SU(3) charges so this simple exercise is directly relevant to understanding confinement in QCD.