Instantons on multi-Taub-NUT Spaces I: Asymptotic Form and Index Theorem

TL;DR

This paper analyzes anti-self-dual Yang-Mills connections on multi-Taub-NUT spaces, establishing decay rates and computing the Dirac operator index, laying groundwork for understanding instantons in this geometric setting.

Contribution

It provides the first detailed analysis of decay rates and index computations for instantons on multi-Taub-NUT spaces, advancing the mathematical understanding of these solutions.

Findings

Curvature and harmonic spinors decay at specific rates

Computed the index of the Dirac operator in this setting

Established foundational results for instantons on multi-Taub-NUT spaces

Abstract

We study finite action anti-self-dual Yang-Mills connections on the multi-Taub-NUT space. We establish the curvature and the harmonic spinors decay rates and compute the index of the associated Dirac operator. This is the first in a series of papers proving the completeness of the bow construction of instantons on multi-Taub-NUT spaces and exploring it in detail.