Nonabelian Superconductors: Vortices and Confinement in ${\cal N}=2$ SQCD

TL;DR

This paper investigates nonabelian vortices in ${ m SU}(N)$ gauge theories, especially in ${ m ext{SU}}(3)$ ${ m ext{SQCD}}$, revealing their zero modes, effective world-sheet theories, and implications for confinement and duality.

Contribution

It provides a detailed semi-classical analysis of nonabelian vortices in ${ m ext{SU}}(3)$ ${ m ext{SQCD}}$, including their zero modes and effective sigma models, advancing understanding of confinement mechanisms.

Findings

Vortices acquire exact zero modes generating global $SU(2)_{C+F}$ rotations.

The effective world-sheet theory reduces to an ${ m ext{N}}=2$ O(3) sigma model.

Mirror symmetry indicates the dual SU(2) remains unbroken.

Abstract

We study nonabelian vortices (flux tubes) in SU(N) gauge theories, which are responsible for the confinement of (nonabelian) magnetic monopoles. In particular a detailed analysis is given of ${\cal N}=2$ SQCD with gauge group SU(3) deformed by a small adjoint chiral multiplet mass. Tuning the bare quark masses (which we take to be large) to a common value $m$, we consider a particular vacuum of this theory in which an SU(2) subgroup of the gauge group remains unbroken. We consider $5 \ge N_f \ge 4$ flavors so that the SU(2) sub-sector remains non asymptotically free: the vortices carrying nonabelian fluxes may be reliably studied in a semi-classical regime. We show that the vortices indeed acquire exact zero modes which generate global rotations of the flux in an $SU(2)_{C+F}$ group. We study an effective world-sheet theory of these orientational zero modes which reduces to an ${\cal N}=2$ O(3) sigma model in (1+1) dimensions. Mirror symmetry then teaches us that the dual SU(2) group is not dynamically broken.