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.
Highlights
Non-Abelian vortex strings were first found in N 1⁄4 2 supersymmetric QCD (SQCD) with gauge group UðNÞ and Nf 1⁄4 N flavors of quark hypermultiplets [1,2,3,4]; see [5,6,7,8] for reviews
One promising approach is to deform N 1⁄4 2 SQCD by the mass μ of the adjoint matter and study what happens to non-Abelian strings upon this deformation. This deformation breaks N 1⁄4 2 supersymmetry, and in the limit of μ → ∞ the bulk theory flows to N 1⁄4 1 SQCD
In Ref. [16] the world sheet theory living on the non-Abelian string in the μ-deformed SQCD was found, and it was shown that it flows to the nonsupersymmetric CPðN − 1Þ model in the limit of large μ
Summary
Non-Abelian vortex strings were first found in N 1⁄4 2 supersymmetric QCD (SQCD) with gauge group UðNÞ and Nf 1⁄4 N flavors of quark hypermultiplets [1,2,3,4]; see [5,6,7,8] for reviews. [16] the world sheet theory living on the non-Abelian string in the μ-deformed SQCD was found, and it was shown that it flows to the nonsupersymmetric CPðN − 1Þ model in the limit of large μ. In this paper we use the large N approximation to study a phase structure of the world sheet theory on the nonAbelian string in μ-deformed SQCD with respect to the deformation parameter μ and quark mass differences Δm. In the second strong coupling phase at large μ quasivacua are distinguished by the value of the constant electric field This phase is qualitatively similar to the nonsupersymmetric CPðN − 1Þ model. We will introduce the model that we will be working with, namely the μ-deformed CPðN − 1Þ model which is an effective theory living on the world sheet of non-Abelian string in μ-deformed SQCD [16]
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