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

TL;DR

The authors construct a minimal non-supersymmetric SU($N$)×U(1) Yang–Mills model at weak coupling that supports non-Abelian magnetic flux tubes and confined monopoles, aiming to capture essential QCD-like string dynamics. The effective string world sheet is described by a massive CP$(N-1)$ model, with a shared $\theta$-angle between bulk and world sheet, enabling a detailed study of the confinement mechanism and its dependence on a mass parameter $m$. A phase transition at $m_*\sim\Lambda$ separates Abelian confinement with $Z_N$-degenerate strings from non-Abelian confinement with split tensions and two-dimensional monopole confinement; the transition is analyzed at large $N$, including a special solvable SU(2)×U(1) case. The paper also develops a dual description where confined monopoles attach to strings as gluelumps, computes string tensions and decay rates, and discusses implications for QCD-string phenomenology and the role of $Z_N$ symmetry.

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.

Figures (9)

• Figure 1: The vacuum structure of $CP(N-1)$ model at $\theta =0$.
• Figure 2: The vacuum structure of $CP(N-1)$ model at $\theta = \pi$.
• Figure 3: Linear confinement of the $n$-$n^*$ pair. The solid straight line represents the string. The dashed line shows the vacuum energy density (normalizing ${\cal E}_0$ to zero).
• Figure 4: Breaking of the excited string through the $n$-$n^*$ pair creation. The dashed line shows the vacuum energy density.
• Figure 5: The function $1 + {\cal E}_{0, \pm 1}/[ (6 N\, \Lambda^2 )\pi^{-1}]$ in the units $\pi^2/(2N^2)$ versus $\theta /\pi$.