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We study the dynamics of non-Abelian vortex strings supported in ${\mathcalN}=2$ supersymmetric QCD with the U$(N)$ gauge group and $N_f=N$ quark flavorsdeformed 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 describedby 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 thenon-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 thedeformation parameter $\mu$ and quark mass differences. The phases include twostrong coupling phases and two Higgs phases. In particular, the Higgs phase atsmall $\mu$ supports CP$(N-1)$ model kinks representing confined monopoles ofthe bulk QCD, while in the large-$\mu$ Higgs phase monopoles disappear.

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