A Generalized Construction for Lumps and Non-Abelian Vortices

TL;DR

This paper develops a comprehensive method to construct non-Abelian vortex solutions in a general gauge theory with a fully-Higgsed vacuum, establishing a link to lumps in a sigma-model and deriving the vortex moduli space.

Contribution

It introduces a generalized construction for non-Abelian vortices in theories with arbitrary simple gauge groups and U(1), connecting vortex solutions to sigma-model lumps and elucidating the moduli space.

Findings

Constructed the general vortex solution in a fully-Higgsed, color-flavor locked vacuum.

Established a strict correspondence between vortices and lumps in the associated sigma-model.

Derived the vortex moduli space from this correspondence.

Abstract

We construct the general vortex solution in a fully-Higgsed, color-flavor locked vacuum of a non-Abelian gauge theory, where the gauge group is taken to be the product of an arbitrary simple group and U(1), with a Fayet-Iliopoulos term. The strict correspondence between vortices and lumps in the associated Non-Linear Sigma-Model which arise in the limit of strong coupling is pointed out. The construction of the vortex moduli space is derived here as a consequence of this correspondence.