Motion on moduli spaces with potentials

TL;DR

This paper extends the geodesic approximation for BPS solitons by incorporating potentials, analyzing the complex dynamics of dyonic instantons with both analytical and numerical methods, highlighting the role of nonzero-modes.

Contribution

It introduces a potential term into the moduli space dynamics for a broader class of models and provides a detailed analysis of dyonic instanton dynamics including nonzero-modes.

Findings

Potential terms are essential for quarter-BPS state dynamics.

Nonzero-modes significantly influence the qualitative behavior of instantons.

Analytical and numerical methods reveal new dynamical phenomena.

Abstract

In the limit of small velocities, the dynamics of half-BPS Yang-Mills-Higgs solitons can be described by the geodesic approximation. Recently, it has been shown that quarter-BPS states require the addition of a potential term to this approximation. We explain the logic behind this modification for a larger class of models and then analyse in detail the dynamics of two five-dimensional dyonic instantons, using both analytical and numerical techniques. Nonzero-modes are shown to play a crucial role in the analysis of these systems, and we explain how these modes lead to qualitatively new types of dynamics.