We consider non-Abelian semilocal strings (vortices or vortex strings) arising in N=2 supersymmetric U(N) gauge theory with Nf=N+N∼ matter hypermultiplets in the fundamental representation (quarks) and a Fayet-Iliopoulos term ξ. 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 (ln L)→, 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(Nf-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(Nf-1) model and zn model are different. Still, their quasiclassical excitation spectra coincide.
|Original language||English (US)|
|Journal||Physical Review D - Particles, Fields, Gravitation and Cosmology|
|State||Published - Jun 10 2011|