We study non-Abelian vortex strings in four-dimensional (4D) N=2 supersymmetric QCD with the U(N=2) gauge group and Nf=4 flavors of quark hypermultiplets. It has recently been shown that these vortices behave as critical superstrings. The spectrum of closed string states in the associated string theory was found and interpreted as a spectrum of hadrons in 4D N=2 supersymmetric QCD. In particular, the lowest string state appears to be a massless Bogomol'nyi-Prasad-Sommerfield (BPS) "baryon."Here we show the occurrence of this stringy baryon using a purely field-theoretic method. To this end we study the conformal world-sheet theory on the non-Abelian string - the so-called weighted N=(2,2) supersymmetric CP model. Its target space is given by the six-dimensional noncompact Calabi-Yau space Y6, the conifold. We use a mirror description of the model to study the BPS kink spectrum and its transformations on curves (walls) of marginal stability. Then we use the 2D-4D correspondence to show that the deformation of the complex structure of the conifold is associated with the emergence of a nonperturbative Higgs branch in 4D theory which opens up at strong coupling. The modulus parameter on this Higgs branch is the vacuum expectation value of the massless BPS baryon previously found in string theory.
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Useful discussions with E. Gerchkovitz and A. Karasik are acknowledged. The work of M. S. is supported in part by DOE Grant No. DE-SC0011842. The work of A. Y. was supported by William I. Fine Theoretical Physics Institute, University of Minnesota and by Russian Foundation for Basic Research Grant No. 18-02-00048a. The work of E. I. was supported in part by the Foundation for the Advancement of Theoretical Physics and Mathematics “BASIS” according to the Research Project No. 19-1-5-106-1, and by Russian Foundation for Basic Research Grant No. 18-02-00048a.