Studying Critical String Emerging from Non-Abelian Vortex in Four Dimensions

Recently a special vortex string was found [5] in a class of soliton vortices supported in four-dimensional Yang-Mills theories that under certain conditions can become infinitely thin and can be interpreted as a critical ten-dimensional string. The appropriate bulk Yang-Mills theory has the U(2) gauge group and the Fayet-Iliopoulos term. It supports semilocal non-Abelian vortices with the world-sheet theory for orientational and size moduli described by the weighted CP(2,2) model. The full target space is R_4\times Y_6 where Y_6 is a non-compact Calabi-Yau space. We study the above vortex string from the standpoint of string theory, focusing on the massless states in four dimensions. In the generic case all massless modes are non-normalizable, hence, no massless gravitons or vector fields are predicted in the physical spectrum. However, at the selfdual point (at strong coupling) weighted CP(2,2) admits deformation of the complex structure, resulting in a single massless hypermultiplet in the bulk. We interpret it as a composite "baryon."