Effective world-sheet theory for non-Abelian semilocal strings in N=2 supersymmetric QCD

We consider non-Abelian semilocal strings (vortices or vortex strings) arising in N = 2 super-symmetric U(N) gauge theory with N-f = N + (N) over tilde matter hypermultiplets in the fundamental representation (quarks) and a Fayet-Iliopoulos term xi. We present, for the first time ever, a systematic field-theoretic derivation of the world-sheet theory for such strings, describing dynamics of both orientational and size-zero modes. Our derivation is complete in the limit (lnL) -> infinity ! 1, where L is an infrared regulator in the transverse plane. In this limit, the world-sheet theory is obtained exactly. It is presented by a so-far unknown N = 2 two-dimensional sigma model, to which we refer as the zn model, with or without twisted masses. Alternative formulations of the zn model are worked out: conventional and extended gauged formulations and a geometric formulation. We compare the exact metric of the zn model with that of the weighted CP(N-f - 1) model conjectured by Hanany and Tong, through D branes, as the world-sheet theory for the non-Abelian semilocal strings. The Hanany-Tong setup has no parallel for the field-theoretic infrared parameter, and metrics of the weighted CP(N-f - 1) model and zn model are different. Still, their quasiclassical excitation spectra coincide.