Boundary metrics on soliton moduli spaces

TL;DR

This paper explores boundary metrics on soliton moduli spaces, demonstrating that geodesics of these metrics can effectively approximate soliton dynamics in systems where traditional methods fail.

Contribution

It introduces a general framework for boundary metrics on soliton moduli spaces and shows their effectiveness in modeling soliton dynamics in lower-dimensional systems.

Findings

Boundary metrics can approximate soliton dynamics effectively.

Geodesics of boundary metrics align with full nonlinear simulations.

Applicable to systems where the traditional moduli space metric is not finite.

Abstract

The geodesic approximation is a powerful method for studying the dynamics of BPS solitons. However, there are systems, such as BPS monopoles in three-dimensional hyperbolic space, where this approach is not applicable because the moduli space metric defined by the kinetic energy is not finite. In the case of hyperbolic monopoles, an alternative metric has been defined using the abelian connection on the sphere at infinity, but its relation to the dynamics of hyperbolic monopoles is unclear. Here this metric is placed in a more general context of boundary metrics on soliton moduli spaces. Examples are studied in systems in one and two space dimensions, where it is much easier to compare the results with simulations of the full nonlinear field theory dynamics. It is found that geodesics of the boundary metric provide a reasonable description of soliton dynamics.