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

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.

49 pages, 25 figures

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Cited by in corpus (3)

• Some comments about emission channels of non abelian vortices
• Dynamics of non-Abelian strings in supersymmetric gauge theories
• Large-$N$ Solution and Effective Action of "Twisted-Mass'' Deformed $\mathbb{CP}(N-1)$ Model