A hyperbolic analogue of the Atiyah-Hitchin manifold

TL;DR

This paper constructs a hyperbolic analogue of the Atiyah-Hitchin manifold by calculating the boundary metric on the moduli space of symmetric charge two SU(2) monopoles in hyperbolic space, using twistor methods.

Contribution

It introduces a new hyperbolic version of the Atiyah-Hitchin manifold and computes its boundary metric via a twistor approach, extending monopole moduli space analysis.

Findings

Derived the boundary metric in terms of elliptic integrals.

Extended the understanding of monopole moduli spaces to hyperbolic geometry.

Provided explicit calculations for symmetric charge two monopoles.

Abstract

The Atiyah-Hitchin manifold is the moduli space of parity inversion symmetric charge two SU(2) monopoles in Euclidean space. Here a hyperbolic analogue is presented, by calculating the boundary metric on the moduli space of parity inversion symmetric charge two SU(2) monopoles in hyperbolic space. The calculation of the metric is performed using a twistor description of the moduli space and the result is presented in terms of standard elliptic integrals.