Kinks, chains, and loop groups in the CP^n sigma models

TL;DR

This paper investigates topological solitons called kinks and chains in CP^n sigma models, analyzing their constituent structures using Lie algebra techniques, and drawing parallels with monopoles and calorons in gauge theories.

Contribution

It introduces a detailed analysis of kink and chain solutions in CP^n sigma models, highlighting their constituent structures and connections to gauge theory solitons.

Findings

Kinks are independent of one coordinate up to target space rotation.

Chains are periodic in one coordinate up to target space rotation.

Constituent structures resemble monopoles and calorons in gauge theories.

Abstract

We consider topological solitons in the CP^n sigma models in two space dimensions. In particular, we study "kinks", which are independent of one coordinate up to a rotation of the target space, and "chains", which are periodic in one coordinate up to a rotation of the target space. Kinks and chains both exhibit constituents, similar to monopoles and calorons in SU(n) Yang-Mills-Higgs and Yang-Mills theories. We examine the constituent structure using Lie algebras.