TL;DR
This paper explores the construction of ALE and Taub-NUT hyper-Kahler four-manifolds using D-branes, providing new insights into instantons on these spaces and their applications in M-theory.
Contribution
It offers a D-brane derivation for Taub-NUT spaces and refines the analysis of instantons using D-brane probes, linking hyper-Kahler quotients to string theory.
Findings
D-brane derivation of Taub-NUT spaces
Refined instanton analysis on Taub-NUT spaces
Application to M-theory
Abstract
ALE and Taub-NUT (or ALF) hyper-Kahler four-manifolds can be naturally constructed as hyper-Kahler quotients. In the ALE case, this construction has long been understood in terms of D-branes; here we give a D-brane derivation in the Taub-NUT case. Likewise, instantons on ALE spaces and on Taub-NUT spaces have ADHM-like constructions related to hyper-Kahler quotients. Here we refine the analysis in the Taub-NUT case by making use of a D-brane probe, and give an application to M-theory.
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