A New and Elementary CP^n Dyonic Magnon

TL;DR

This paper introduces a new elementary dyonic magnon solution in CP^n models using the dressing transformation, unifying and generalizing known solutions including Dorey's dyonic magnon.

Contribution

It presents a novel dyonic magnon solution in CP^n, derived via dressing transformations, and connects it to existing solutions and sine-Gordon theories.

Findings

New elementary dyonic CP^n magnon solution

Unification of known solutions as special cases or composites

Direct generation of Dorey's dyonic magnon in S^n sigma model

Abstract

We show that the dressing transformation method produces a new type of dyonic CP^n magnon in terms of which all the other known solutions are either composites or arise as special limits. In particular, this includes the embedding of Dorey's dyonic magnon via an RP^3 subspace of CP^n. We also show how to generate Dorey's dyonic magnon directly in the S^n sigma model via the dressing method without resorting to the isomorphism with the SU(2) principle chiral model when n=3. The new dyon is shown to be either a charged dyon or topological kink of the related symmetric-space sine-Gordon theories associated to CP^n and in this sense is a direct generalization of the soliton of the complex sine-Gordon theory.