Instanton Moduli and Topological Soliton Dynamics

TL;DR

This paper explores how the dynamics of various solitons can be approximated by finite-dimensional models derived from instanton moduli spaces, extending the Atiyah-Manton approach beyond Skyrmions.

Contribution

It demonstrates the construction of finite-dimensional models from instanton moduli spaces for sine-Gordon solitons, providing a new approximation framework for soliton dynamics.

Findings

Finite-dimensional models approximate sine-Gordon soliton dynamics.

Comparison shows good agreement with exact solutions.

Extends instanton-based approximation methods to other solitons.

Abstract

It has been proposed by Atiyah and Manton that the dynamics of Skyrmions may be approximated by motion on a finite dimensional manifold obtained from the moduli space of SU(2) Yang-Mills instantons. Motivated by this work we describe how similar results exist for other soliton and instanton systems. We describe in detail two examples for the approximation of the infinite dimensional dynamics of sine-Gordon solitons by finite dimensional dynamics on a manifold obtained from instanton moduli. In the first example we use the moduli space of CP1 instantons and in the second example we use the moduli space of SU(2) Yang-Mills instantons. The metric and potential functions on these manifolds are constructed and the resulting dynamics is compared with the explicit exact soliton solutions of the sine-Gordon theory.