What becomes of semilocal non-Abelian strings in N=1 supersymmetric QCD

We study non-Abelian vortex strings in N = 2 supersymmetric QCD with the gauge group U(N) deformed by the mass mu of the adjoint matter. This deformation breaks N = 2 supersymmetry down to N = 1 and in the limit of large mu the theory flows to N = 1 QCD. Non-Abelian strings in addition to translational zero modes have orientation moduli. In the N = 2 limit of small mu the dynamics of orientational moduli is described by the two-dimensional CP(N - 1) model for QCD with N-f = N flavors of quark hypermultiplets. For the case of N-f > N the non-Abelian string becomes semilocal developing additional size moduli that modify the effective two-dimensional sigma-model on the string making its target space noncompact. In this paper we consider the mu-deformed theory with N-f > N eventually making mu large. We show that size moduli develop a potential that forces the string transverse size to shrink. Eventually in the large mu limit size moduli decouple and the effective theory on the string reduces to the CP(N - 1) model. We also comment on physics of confined monopoles.