Non-Abelian Vortex in Four Dimensions as a Critical Superstring

We discuss recent progress in describing a certain non-Abelian vortex string as a critical superstring on a conifold and clarify some subtle points. This particular solitonic vortex is supported in four-dimensional N=2 supersymmetric QCD with the U(2) gauge group, N_f=4 quark flavors and the Fayet-Iliopoulos term. Under certain conditions the non-Abelian vortex can become infinitely thin and can be interpreted as a critical ten-dimensional superstring. In addition to four translational moduli the non-Abelian vortex under consideration carries six orientational and size moduli. The vortex moduli dynamics are described by a two-dimensional sigma model with the target space {R}^4\times Y_6 where Y_6 is a non-compact Calabi-Yau conifold. The closed string states which emerge in four dimensions (4D) are identified with hadrons of 4D bulk N=2 QCD. It turns out that most of the states arising from the ten-dimensional graviton spectrum are non-dynamical in 4D. A single dynamical massless hypermultiplet associated with the deformation of the complex structure of the conifold is found. It is interpreted as a monopole-monopole baryon of the 4D theory (at strong coupling).