Effective World-Sheet Theory for Non-Abelian Semilocal Strings in N = 2 Supersymmetric QCD

TL;DR

This paper derives an exact world-sheet theory for non-Abelian semilocal strings in N=2 supersymmetric QCD, introducing the novel zn model and comparing it to the weighted CP(Nf-1) model.

Contribution

It provides the first systematic field-theoretic derivation of the world-sheet theory for non-Abelian semilocal strings, introducing the zn model and analyzing its properties.

Findings

Exact metric of the zn model derived and compared with the weighted CP(Nf-1) model.

Quasiclassical excitation spectra of the two models coincide.

Different IR parameters and metrics, but similar spectra, are established.

Abstract

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 {\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, ln(L)\rightarrow \infty, where L is an infrared (IR) 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 set-up has no parallel for the field-theoretic IR parameter and metrics of the weighted CP(Nf-1) model and zn model are different. Still their quasiclassical excitation spectra coincide.