The Semi-Classical Spectrum of Solitons and Giant Magnons

TL;DR

This paper reviews semi-classical quantization of solitons and giant magnons in symmetric space sine-Gordon theories, revealing their quantum states and differences in their spectral towers within the context of string theory.

Contribution

It provides a semi-classical quantization framework for solitons and giant magnons, highlighting their quantum spectra and the role of Chern-Simons mechanics on moduli spaces.

Findings

Both solitons and magnons lead to Chern-Simons quantum mechanics on the moduli space.

Quantization shows solitons have a finite tower of states, while magnons have an infinite tower.

States form symmetric representations of the SO(4) symmetry group.

Abstract

In this note, we summarize recent progress in constructing and then semi-classically quantizing solitons, or non-abelian Q-balls, in the symmetric space sine-Gordon theories. We then consider the images of these solitons in the related constrained sigma model, which are the dyonic giant magnons on the string theory world-sheet. Focussing on the case of the symmetric space S^5, we perform a semi-classical quantization of the solitons and magnons and show that both lead to Chern-Simons quantum mechanics on the internal moduli space which is a real Grassmannian SO(4)/SO(2)xSO(2) but---importantly---with a different coupling constant. Quantizing this system shows that both the Q-balls and magnons come in a tower of states transforming in symmetric representations of the SO(4) symmetry group; however, the former come in a finite tower whereas the latter come in the well-known infinite tower of dyonic giant magnons.