Long-Range Behavior of Dual-Restricted QCD Vacuum

We analyze the geometrical structure of the local non-Abelian gauge theory in terms of the magnetic symmetry, using the resemblance between the non-Abelian gauge formulations and Einstein's theory of gravitation in a higher dimensional unified space. The mathematical foundation of dual QCD in fiber bundle form is then discussed and used for the analysis of the important problem of color confinement in QCD. The associated Lagrangian formulation in magnetic gauge is shown to lead to dual dynamics due to the emergence of the topological charges of magnetic nature. The dynamical breaking of magnetic symmetry is shown to lead to the magnetic condensation of the QCD vacuum. A state of the dual superconductivity in the QCD vacuum is then shown to evolve which ultimately pushes the QCD vacuum to the confining phase. The flux tube structure of the magnetically condensed QCD vacuum is analyzed by computing the asymptotic string solutions of the field equations. The energy content of such confining structures is computed and analyzed in terms of its logarithmic and linear nature.