A.V. Yung (PNPI)

 

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 behave as 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 tau-topological 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 R^4 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 N = 2 QCD. 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)