Monads for Instantons and Bows

TL;DR

This paper explores the complex geometric relationships between instantons on Taub-NUT space and bow solutions, establishing a correspondence through monads and various geometric transforms.

Contribution

It introduces monads that encode instantons and bow solutions, demonstrating a one-to-one correspondence between them via complex geometry techniques.

Findings

Established equivalences between instantons and bow solutions.

Constructed monads encoding each solution type.

Proved a one-to-one correspondence between instantons and bow solutions.

Abstract

Instantons on the Taub-NUT space are related to `bow solutions' via a generalization of the ADHM-Nahm transform. Both are related to complex geometry, either via the twistor transform or via the Kobayashi-Hitchin correspondence. We explore various aspects of this complex geometry, exhibiting equivalences. For both the instanton and the bow solution we produce two monads encoding each of them respectively. Identifying these monads we establish the one-to-one correspondence between the instanton and the bow solution.