Non-Abelian vortex in four dimensions as a critical string on a conifold

Non-Abelian vortex strings supported in a certain four-dimensional N=2 Yang-Mills theory with fundamental matter were shown [1] to become critical superstrings. In addition to translational moduli, the non-Abelian strings under consideration carry orientational and size moduli. Their dynamics is described by the two-dimensional sigma model whose target space is a tautological bundle over the complex projective space. For the N=2 theory with the U(2) gauge group and four fundamental hypermultiplets, there are six orientational and size moduli. After combining with four translational moduli, they form a ten-dimensional target space, which is required for a superstring to be critical. For the theory in question, the target space of the sigma model is C2×Y6, where Y6 is a conifold. We study closed string states which emerge in four dimensions (4D) and identify them with hadrons of the 4D bulk N=2 theory. It turns out that most of the states arising from the ten-dimensional graviton spectrum are nondynamical in 4D. We find a single dynamical massless hypermultiplet associated with the deformation of the complex structure of the conifold. We interpret this degree of freedom as a monopole-monopole baryon of the 4D theory (at strong coupling).