Composite non-Abelian Flux Tubes in N=2 SQCD

TL;DR

This work analyzes composite non-Abelian flux tubes in $\,\mathcal{N}=2$ $U(2)$ SQCD with a Fayet–Iliopoulos term, revealing that a coincident two-string configuration possesses a rich internal moduli space. The authors explicitly construct a six-parameter BPS solution for $R=0$ and show the internal moduli space is the discrete quotient $\mathbb{CP}^2/\mathbb{Z}_2$, with special limits ($\alpha=0$ and $\alpha=\pi$) reproducing the Abelian $(2,0)$, $(0,2)$ and $(1,1)$ strings. Through field-theory analysis and brane constructions, they connect this 2-string moduli space to a 1+1D $\mathcal{N}=2$ $\mathbb{CP}^1$ sigma model on the worldsheet and discuss the spectrum of confined monopoles in various parametric regimes, including where Seiberg–Witten dynamics governs the 4D bulk. The results illuminate how composite non-Abelian flux tubes interpolate between elementary strings and provide a topological framework for understanding confinement phenomena in this setting, while highlighting open questions about the exact worldsheet metric on $\mathcal{T}$.

Abstract

Composite non-Abelian vortices in N=2 supersymmetric U(2) SQCD are investigated. The internal moduli space of an elementary non-Abelian vortex is CP^1. In this paper we find a composite state of two coincident non-Abelian vortices explicitly solving the first order BPS equations. Topology of the internal moduli space T is determined in terms of a discrete quotient CP^2/Z_2. The spectrum of physical strings and confined monopoles is discussed. This gives indirect information about the sigma model with target space T.

Figures (11)

• Figure 1: Lattice of $(p,k)$ vortices.
• Figure 2: Lattice of possible Abelian vortices. In the non-Abelian case $m_1=m_2=m$ there is a moduli space interpolating between different element of the lattice.
• Figure 3: It is always possible to align $\vec{n}_1$ with the $\tau_3$ axis and put $\vec{n}_2$ on the $\tau_3-\tau_1$ plane. The angle between $\vec{n}_1$ and $\vec{n}_2$ is $\alpha$. A global $SU(2)_{C+F}$ rotation introduced three extra angles.
• Figure 4: $\kappa(r)$ (left): $z_1(r)$ (center), $z_2(r)$ (right), at $\alpha=0$ (green), $\alpha=\frac{\pi}{2}$ (red), $\alpha=\pi$ (blue).
• Figure 5: f(r) (left): $f_3(r)$ (center), $g(r)$ (right), at $\alpha=0$ (green), $\alpha=\frac{\pi}{2}$ (red), $\alpha=\pi$ (blue).