Confining solutions of SU(3) Yang-Mills theory

Abstract

Spherically and cylindrically symmetric solutions of SU(3) Yang-Mills theory are found, whose gauge potentials have confining properties. The spherically symmetric solutions give field distributions which have a spherical surface on which the gauge fields become infinite (which is similar to bag models of confinement), and the other solution has a potential which increases at large distances. The cylindrically symmetric solution describes a classical field "string" (flux tube) of the kind which is expected to form between quarks in the dual superconductor picture of confinement. These solutions with classical confining behaviour appear to be typical solutions for the classical SU(3) Yang-Mills equations. This implies that the confining properties of the classical SU(3) Yang-Mills theory are general properties of this theory.