Moduli Spaces of Instantons on the Taub-NUT Space

TL;DR

This paper develops a new mathematical framework for describing instantons on the Taub-NUT space using ADHM-Nahm data and Bow Diagrams, providing explicit metrics and linking to string theory brane configurations.

Contribution

It introduces a novel description of instanton moduli spaces on Taub-NUT space via hyperkahler quotients and explicit metrics, connecting gauge theory and string theory.

Findings

Explicit metric for one SU(2) instanton moduli space

Representation of moduli spaces as hyperkahler quotients

Connection between instantons, Bow Diagrams, and string theory branes

Abstract

We present ADHM-Nahm data for instantons on the Taub-NUT space and encode these data in terms of Bow Diagrams. We study the moduli spaces of the instantons and present these spaces as finite hyperkahler quotients. As an example, we find an explicit expression for the metric on the moduli space of one SU(2) instanton. We motivate our construction by identifying a corresponding string theory brane configuration. By following string theory dualities we are led to supersymmetric gauge theories with impurities.