# Moduli spaces of SO(8) instantons on smooth ALE spaces as Higgs branches of 4d $$\mathcal{N}$$ = 2 supersymmetric theories

Journal of High Energy Physics, Jun 2014

The worldvolume theory of D3-branes probing four D7-branes and an O7-plane on $$\mathbb{C}$$ 2/$$\mathbb{Z}$$ 2 is given by a supersymmetric USp × USp gauge theory. We demonstrate that, at least for a particular choice of the holonomy at infinity, we can go to a dual description of the gauge theory, where we can add a Fayet-Iliopoulos term describing the blowing-up of the orbifold to the smooth ALE space. This allows us to express the moduli space of SO(8) instantons on the smooth ALE space as a hyperkähler quotient of a flat space times the Higgs branch of a class S theory. We also discuss a generalization to $$\mathbb{C}$$ 2/$$\mathbb{Z}$$ 2n , and speculate how to extend the analysis to bigger SO groups and to ALE spaces of other types.

This is a preview of a remote PDF: https://link.springer.com/content/pdf/10.1007%2FJHEP06%282014%29056.pdf

Yuji Tachikawa. Moduli spaces of SO(8) instantons on smooth ALE spaces as Higgs branches of 4d $$\mathcal{N}$$ = 2 supersymmetric theories, Journal of High Energy Physics, 2014, 56, DOI: 10.1007/JHEP06(2014)056