Non-Abelian Meissner Effect in Yang--Mills Theories at Weak Coupling

TL;DR

This paper introduces a weak-coupling Yang--Mills model that exhibits a phase transition between Abelian and non-Abelian confinement, featuring non-Abelian flux tubes and monopoles, with implications for understanding QCD strings.

Contribution

It presents a novel weak-coupling model demonstrating non-Abelian confinement and a phase transition governed by a Z_N symmetry, with explicit calculations of string tensions and decay rates.

Findings

Identifies a phase transition at a critical mass parameter m_*

Shows spontaneous breaking and restoration of Z_N symmetry

Calculates tensions and decay rates of non-Abelian strings

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_* of order of 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 >> 1.