Explicit Construction of Yang-Mills Instantons on ALE Spaces

TL;DR

This paper provides an explicit construction of Yang-Mills instantons on ALE spaces, including abelian and non-abelian cases, with detailed analysis of their moduli spaces, topological features, and specific solutions on Eguchi-Hanson backgrounds.

Contribution

It introduces a generalized 't Hooft ansatz for SU(2) instantons on ALE spaces and explicitly solves ADHM equations for specific Chern classes.

Findings

Explicit instanton solutions on ALE spaces.

Partition function calculations for Maxwell theories.

Topological and moduli space characterizations.

Abstract

We describe the explicit construction of Yang-Mills instantons on ALE spaces, following the work of Kronheimer and Nakajima. For multicenter ALE metrics, we determine the abelian instanton connections which are needed for the construction in the non-abelian case. We compute the partition function of Maxwell theories on ALE manifolds and comment on the issue of electromagnetic duality. We discuss the topological characterization of the instanton bundles as well as the identification of their moduli spaces. We generalize the 't Hooft ansatz to SU(2) instantons on ALE spaces and on other hyper-Kahler manifolds. Specializing to the Eguchi-Hanson gravitational background, we explicitly solve the ADHM equations for SU(2) gauge bundles with second Chern class 1/2, 1 and 3/2.