An 8-dimensional Taub-NUT-like hyper-K\"ahler metric in harmonic superspace formalism

TL;DR

This paper derives an 8-dimensional hyper-K"ahler metric using harmonic superspace formalism, generalizing the Taub-NUT manifold and linking it to monopole dynamics through Hamiltonian reduction.

Contribution

It introduces a new 8-dimensional hyper-K"ahler metric via harmonic superspace, extending the Taub-NUT solution and connecting it to monopole moduli space.

Findings

Derived an explicit 8D hyper-K"ahler metric

Identified the metric as a generalization of Taub-NUT

Proposed equivalence to a known monopole metric

Abstract

Using the harmonic superspace formalism, we find the metric of a certain 8-dimensional manifold. This manifold is not compact and represents an 8-dimensional generalization of the Taub-NUT manifold. Our conjecture is that the metric that we derived is equivalent to the known metric possessing a discrete $Z_2$ isometry, which may be obtained from the metric describing the dynamics of four BPS monopoles by Hamiltonian reduction.