Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

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

Derek Harland

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.

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

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.

Paper Structure

This paper contains 7 sections, 46 equations, 3 figures.

Table of Contents

  1. Introduction
  2. The $\mathbb{CP}^n$ sigma models
  3. Multi-kinks
  4. Chains
  5. Loop groups
  6. A chain as a loop group multi-kink
  7. Summary and open problems

Figures (3)

  • Figure 1: The $\mathbb{CP}^2$ multi-kink realised as an adjoint orbit in the Lie algebra of $SU(3)$.
  • Figure 2: The Dynkin diagrams of various Lie groups and their loop groups
  • Figure 3: The charge 1 $\mathbb{CP}^1$ chain realised as an adjoint orbit in the Lie algebra of the loop groop