Topology of QCD vacuum and color confinement

Abstract

Using the magnetic symmetry structure of non-Abelian gauge theories of the Yang–Mills type, the mathematical foundation of dual chromodynamics in fiber-bundle form is discussed. The dual gauge potential in its restricted form is constructed in terms of magnetic vectors on global sections, which has been shown to lead the dual dynamics between topological charges and color isocharges. Constructing the Lagrangian for such dual theory, the dynamical breaking of magnetic symmetry by an effective potential is shown to push the QCD vacuum in a confining phase. The dynamical structure of the theory is investigated by deriving the field equations associated with the confining phase. The associated flux-tube structure responsible for the confinement is analyzed by computing the asymptotic string solutions of the field equations under cylindrical symmetry. Using the confining part of the dual restricted Lagrangian, the finite string energy per unit length is calculated and its implications on color confinement are discussed. PACS Nos.: 11.38Aw, 14.80Hv, 11.30Jw