Inversion symmetric 3-monopoles and the Atiyah-Hitchin manifold

TL;DR

This paper studies symmetric 3-monopoles, showing their moduli space forms an Atiyah-Hitchin submanifold, and uses numerical methods to analyze monopole energy densities along specific geodesics, enhancing understanding of their dynamics.

Contribution

It identifies the moduli space of inversion symmetric 3-monopoles as an Atiyah-Hitchin submanifold and applies numerical ADHMN techniques to explore their energy densities and dynamics.

Findings

Moduli space of symmetric 3-monopoles is an Atiyah-Hitchin submanifold.

Numerical computations of monopole energy densities along geodesics.

Insights into 3-monopole dynamics from 2-monopole results.

Abstract

We consider 3-monopoles symmetric under inversion symmetry. We show that the moduli space of these monopoles is an Atiyah-Hitchin submanifold of the 3-monopole moduli space. This allows what is known about 2-monopole dynamics to be translated into results about the dynamics of 3-monopoles. Using a numerical ADHMN construction we compute the monopole energy density at various points on two interesting geodesics. The first is a geodesic over the two-dimensional rounded cone submanifold corresponding to right angle scattering and the second is a closed geodesic for three orbiting monopoles.