Towards a theory of the QCD string

We construct a new model of four-dimensional relativistic strings with integrable dynamics on the worldsheet. in addition to translational modes this model contains a single massless pseudoscalar worldsheet field — the worldsheet axion. the axion couples to a topological density which counts the self-intersection number of a string. the corresponding coupling is fixed by integrability to $$ q=sqrt{frac{7}{16pi }}approx 0.37 $$ . we argue that this model is a member of a larger family of relativistic non-critical integrable string models. this family includes and extends conventional non-critical strings described by the linear dilaton cft. intriguingly, recent lattice data in su(3) and su(5) gluodynamics reveals the presence of a massive pseudoscalar axion on the worldsheet of confining flux tubes. the value of the corresponding coupling, as determined from the lattice data, is equal to q l ≈ 0.38 ± 0.04.