Reduced dynamics of Ward solitons

TL;DR

This paper studies the reduced dynamics of Ward solitons by analyzing the moduli space of solutions, revealing that approximate solutions follow geodesic motion on a Kähler manifold with vanishing magnetic field, and comparing these with exact solutions.

Contribution

It provides a detailed analysis of the moduli space structure and the dynamics of Ward solitons, highlighting the geometric properties influencing their behavior.

Findings

Magnetic field strength on the moduli space vanishes.

Approximate solutions follow geodesic motion.

Comparison between approximate and exact soliton solutions.

Abstract

The moduli space of static finite energy solutions to Ward's integrable chiral model is the space $M_N$ of based rational maps from $\CP^1$ to itself with degree $N$. The Lagrangian of Ward's model gives rise to a K\"ahler metric and a magnetic vector potential on this space. However, the magnetic field strength vanishes, and the approximate non--relativistic solutions to Ward's model correspond to a geodesic motion on $M_N$. These solutions can be compared with exact solutions which describe non--scattering or scattering solitons.