Scattering of instantons, monopoles and vortices in higher dimensions

Abstract

We consider Yang-Mills theory on manifolds $\mathbb{R}\times X$ with a $d$-dimensional Riemannian manifold $X$ of special holonomy admitting gauge instanton equations. Instantons are considered as particle-like solutions in $d+1$ dimensions whose static configurations are concentrated on $X$. We study how they evolve in time when considered as solutions of the Yang-Millsequations on $\mathbb{R}\times X$ with moduli depending on time $t\in \mathbb{R}$. It is shown that in the adiabatic limit, when the metric in the $X$ direction is scaled down, the classical dynamics of slowly moving instantons corresponds to a geodesic motion in the moduli space $\mathcal{M}$ of gauge instantons on $X$. Similar results about geodesic motion in the moduli space of monopoles and vortices in higher dimensions are briefly discussed.

10 pages; v2: 2 refs. added, published version; v3: typos corrected

References in corpus (3)

• Higher Derivative Corrections to Non-Abelian Vortex Effective Theory
• Sigma-model limit of Yang-Mills instantons in higher dimensions
• Yang-Mills moduli space in the adiabatic limit

Cited by in corpus (2)

• Skyrme model from 6d $\mathcal{N}$= (2,0) theory
• Non-Abelian sigma models from Yang-Mills theory compactified on a circle