Some judiciously chosen 4D Yang-Mills theories with various degree of supersymmetry (including no SUSY) support “Non-Abelian string solitons”, i.e. vortex strings with extra moduli on the string world sheet. The emerging target space theories on the world sheet are non-trivial, implying a number of consequence and novel applications both in HEP and condensed matter. I discuss some of them. For instance, in supersymmetric four-dimensional U(2) gauge theory with two flavors, there are two degenerate strings and an SU(2) doublet of interpolating kinks which are demonstrated to be confined monopoles. There is a unique example of such a theory with four flavors supporting a vortex string with six extra moduli corresponding to a critical string in 10 dimensions on a Calabi-Yau manifold of a spatial form.
 
 
https://lbnl.zoom.us/j/95123239716?pwd=OEY3dW9YNmhLMWZicjBQNEV1SU9tQT09