Magnons, their Solitonic Avatars and the Pohlmeyer Reduction

TL;DR

This paper explores solitons in symmetric space sine-Gordon theories derived via Pohlmeyer reduction, focusing on giant magnons relevant to string theory and introducing new solutions in CP^3.

Contribution

It clarifies the construction of soliton charges, discusses Lagrangian formulations, and demonstrates the dressing method's role in generating solitons, including a new magnon solution in CP^3.

Findings

Dressing transformation produces solitons directly in sigma models and sine-Gordon equations.

A new magnon solution in CP^3 is obtained.

Dressing method does not generate dyonic solutions with non-trivial collective coordinate motion.

Abstract

We study the solitons of the symmetric space sine-Gordon theories that arise once the Pohlmeyer reduction has been imposed on a sigma model with the symmetric space as target. Under this map the solitons arise as giant magnons that are relevant to string theory in the context of the AdS/CFT correspondence. In particular, we consider the cases S^n, CP^n and SU(n) in some detail. We clarify the construction of the charges carried by the solitons and also address the possible Lagrangian formulations of the symmetric space sine-Gordon theories. We show that the dressing, or Backlund, transformation naturally produces solitons directly in both the sigma model and the symmetric space sine-Gordon equations without the need to explicitly map from one to the other. In particular, we obtain a new magnon solution in CP^3. We show that the dressing method does not produce the more general "dyonic" solutions which involve non-trivial motion of the collective coordinates carried by the solitons.