Instantons on multi-Taub-NUT Spaces III: Down Transform, Completeness, and Isometry

TL;DR

This paper establishes a one-to-one correspondence and isometry between instantons on multi-Taub-NUT spaces and bow representations, providing a new geometric understanding of their moduli spaces.

Contribution

It proves the equivalence and isometry between instanton solutions and bow representations on multi-Taub-NUT spaces, advancing geometric analysis in gauge theory.

Findings

Gauge equivalence classes correspond to instantons

An isometry between bow and instanton moduli spaces

Provides a geometric framework for instanton analysis

Abstract

The index bundle of a family of Dirac operators associated to an instanton on a multi-Taub-NUT space forms a bow representation. We prove that the gauge equivalence classes of solutions of this bow representation are in one-to-one correspondence with the instantons. We also prove that this correspondence establishes an isometry of the bow and instanton moduli spaces.