  Non-Abelian vortex strings supported in a certain four-dimensional N=2
Yang-Mills theory with fundamental matter were shown arXiv:1502.00683 to become
critical superstrings. In addition to translational moduli non-Abelian string
under consideration carries orientational and size moduli. Their dynamics is
described by 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 required for a superstring to be critical. For the
theory in question the target space of the sigma model is C^2 x Y_6, where Y_6
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
non-dynamical 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).
