Non-Abelian vortices and monopoles in SO(N) theories

TL;DR

This paper constructs non-Abelian vortex solutions in SO(N) gauge theories with N=2 supersymmetry, explores their moduli, and establishes a correspondence with monopoles through symmetry breaking patterns, extending known SU(N) results.

Contribution

It introduces non-Abelian vortex solutions in SO(N) theories with detailed analysis of their moduli and links to monopoles via hierarchical symmetry breaking, generalizing previous SU(N) findings.

Findings

Vortex solutions exhibit continuous non-Abelian orientational moduli.

Homotopy and flux matching establish monopole-vortex correspondence.

Hints of dual non-Abelian transformation properties among monopoles.

Abstract

Non-Abelian BPS vortex solutions are constructed in N=2 theories with gauge groups SO(N)\times U(1). The model has N_f flavors of chiral multiplets in the vector representation of SO(N), and we consider a color-flavor locked vacuum in which the gauge symmetry is completely broken, leaving a global SO(N)_{C+F} diagonal symmetry unbroken. Individual vortices break this symmetry, acquiring continuous non-Abelian orientational moduli. By embedding this model in high-energy theories with a hierarchical symmetry breaking pattern such as SO(N+2) --> SO(N)\times U(1) --> 1, the correspondence between non-Abelian monopoles and vortices can be established through homotopy maps and flux matching, generalizing the known results in SU(N) theories. We find some interesting hints about the dual (non-Abelian) transformation properties among the monopoles.