Non-Abelian Meissner effect in Yang-Mills theories at weak coupling

Abstract

We present a weak-coupling Yang-Mills model supporting non-Abelian magnetic flux tubes and non-Abelian confined magnetic monopoles. In the dual description the magnetic flux tubes are prototypes of the QCD strings. Dualizing the confined magnetic monopoles we get gluelumps which convert a ``QCD string'' in the excited state to that in the ground state. Introducing a mass parameter $m$ we discover a phase transition between the Abelian and non-Abelian confinement at a critical value $m={m}_{*}\ensuremath{\sim}\ensuremath{\Lambda}$. Underlying dynamics are governed by a ${Z}_{N}$ symmetry inherent to the model under consideration. At $m>{m}_{*}$ the ${Z}_{N}$ symmetry is spontaneously broken, resulting in $N$ degenerate ${Z}_{N}$ (Abelian) strings. At $m<{m}_{*}$ the ${Z}_{N}$ symmetry is restored, the degeneracy is lifted, and the strings become non-Abelian. We calculate tensions of the non-Abelian strings, as well as the decay rates of the metastable strings, at $N\ensuremath{\gg}1$.