Dynamics of non-Abelian strings in the theory interpolating from ${\mathcal N}=2$ to ${\mathcal N}=1$ supersymmetric QCD

TL;DR

This paper investigates the evolution of non-Abelian vortex strings in supersymmetric QCD as it transitions from ${ m N}=2$ to ${ m N}=1$ supersymmetry, revealing a complex phase structure and monopole confinement dynamics.

Contribution

It provides a detailed analysis of the world sheet CP$(N-1)$ model's phase transitions and monopole behavior during the supersymmetry deformation.

Findings

Identification of four distinct phases including two strong coupling and two Higgs phases.

Demonstration that monopoles are confined in the small $\mu$ Higgs phase.

Show that monopoles disappear in the large $\mu$ Higgs phase.

Abstract

We study the dynamics of non-Abelian vortex strings supported in ${\mathcal N}=2$ supersymmetric QCD with the U$(N)$ gauge group and $N_f=N$ quark flavors deformed by the mass $\mu$ of the adjoint matter. In the limit of large $\mu$ the bulk four-dimensional theory flows to ${\mathcal N}=1$ supersymmetric QCD. The dynamics of orientational zero modes of the non-Abelian string is described by the world sheet CP$(N-1)$ model. At $\mu=0$ this model has ${\mathcal N}= \left(2,2\right) $ supersymmetry while at large $\mu$ it flows to the non-supersymmetric CP$(N-1)$ model. We solve the world sheet model in the large $N$ approximation and find a rich phase structure with respect to the deformation parameter $\mu$ and quark mass differences. The phases include two strong coupling phases and two Higgs phases. In particular, the Higgs phase at small $\mu$ supports CP$(N-1)$ model kinks representing confined monopoles of the bulk QCD, while in the large-$\mu$ Higgs phase monopoles disappear.