Moduli spaces with external fields

TL;DR

This paper studies the geometric structures of moduli spaces in a 2+1 dimensional chiral model with a WZW term, showing conditions under which soliton dynamics can be approximated by geodesic motion.

Contribution

It demonstrates that the magnetic field from the WZW term vanishes on certain moduli spaces, enabling a geodesic approximation for soliton dynamics.

Findings

Magnetic field vanishes on Grassmanian-based moduli spaces

Soliton dynamics can be approximated by geodesic motion

Provides geometric insight into moduli space structures

Abstract

We consider the geometric structures on the moduli space of static finite energy solutions to the 2+1 dimensional unitary chiral model with the Wess-Zummino-Witten (WZW) term. It is shown that the magnetic field induced by the WZW term vanishes when restricted to the moduli spaces constructed from the Grassmanian embeddings, so that the slowly moving solitons can in some cases be approximated by a geodesic motion on a space of rational maps from $\CP^1$ to the Grassmanian.