Moduli Spaces of Instantons on the Taub-NUT Space
Sergey A. Cherkis
TL;DR
This work introduces a Bow diagram formalism to encode ADHM–Nahm data for Yang–Mills instantons on Taub-NUT and multi-Taub-NUT spaces, showing that their moduli spaces are finite hyperkähler quotients. By relating the bow data to a Type IIA brane setup and its S-dual impurity theory, the authors connect geometric instanton moduli to string theory constructions and mirror symmetry, including a reciprocity rule between bows. A concrete result is the explicit metric on the moduli space of a single SU(2) instanton on Taub-NUT, interpreted in terms of two monopole-like constituents with relative phase. Generalizations to $U(n)$ gauge groups and multi-Taub-NUT backgrounds are described, together with the link to ADHM on flat space via complex-structure analysis, highlighting a robust equivalence of complex geometries while preserving distinct hyperkähler structures. The approach offers a unifying framework for instanton moduli on curved ALF spaces and clarifies the role of impurities and dualities in their gauge-theoretic realization.
Abstract
We present ADHM-Nahm data for instantons on the Taub-NUT space and encode these data in terms of Bow Diagrams. We study the moduli spaces of the instantons and present these spaces as finite hyperkahler quotients. As an example, we find an explicit expression for the metric on the moduli space of one SU(2) instanton. We motivate our construction by identifying a corresponding string theory brane configuration. By following string theory dualities we are led to supersymmetric gauge theories with impurities.