Non-Abelian Vortices in N=1* Gauge Theory

TL;DR

This paper explores the transformation of Z_2 vortices into non-Abelian strings in N=1* SU(2) gauge theory, analyzing their properties, effective world sheet theory, and monopole confinement mechanisms.

Contribution

It demonstrates the emergence of non-Abelian strings with orientational zero modes and analyzes the effective sigma model and monopole confinement in this context.

Findings

Z_2 vortices become non-Abelian strings with orientational modes

The effective world sheet theory is an O(3) sigma model

Monopoles are confined as meson-like states on the strings

Abstract

We consider the N=1* supersymmetric SU(2) gauge theory and demonstrate that the Z_2 vortices in this theory acquire orientational zero modes, associated with the rotation of magnetic flux inside SU(2) group, and turn into the non-Abelian strings, when the masses of all chiral fields become equal. These non-Abelian strings are not BPS-saturated. We study the effective theory on the string world sheet and show that it is given by two-dimensional non-supersymmetric O(3) sigma model. The confined 't Hooft-Polyakov monopole is seen as a junction of the Z_2-string and anti-string, and as a kink in the effective world sheet sigma model. We calculate its mass and show that besides the four-dimensional confinement of monopoles, they are also confined in the two-dimensional theory: the monopoles stick to anti-monopoles to form the meson-like configurations on the strings they are attached to.