Scattering of instantons, monopoles and vortices in higher dimensions

Abstract

In this paper, we consider Yang–Mills theory on manifolds [Formula: see text] with a [Formula: see text]-dimensional Riemannian manifold [Formula: see text] of special holonomy admitting gauge instanton equations. Instantons are considered as particle-like solutions in [Formula: see text] dimensions whose static configurations are concentrated on [Formula: see text]. We study how they evolve in time when considered as solutions of the Yang–Mills equations on [Formula: see text] with moduli depending on time [Formula: see text]. It is shown that in the adiabatic limit, when the metric in the [Formula: see text] direction is scaled down, the classical dynamics of slowly moving instantons corresponds to a geodesic motion in the moduli space [Formula: see text] of gauge instantons on [Formula: see text]. Similar results about geodesic motion in the moduli space of monopoles and vortices in higher dimensions are briefly discussed.