k strings from various perspectives QCD, lattices, string theory and toy models

I review the status of the issue of the k-string tension in Yang-Mills theory. After a summary of known facts I discuss a weakly coupled four-dimensional Yang-Mills theory that supports non-Abelian strings and can, in certain aspects, serve as a toy model for QCD strings. In the second part of the talk I present original results obtained in a two-dimensional toy model which provides some evidence for the sine formula.