Abstract
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.
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Tachikawa, Y. Moduli spaces of SO(8) instantons on smooth ALE spaces as Higgs branches of 4d \( \mathcal{N} \) = 2 supersymmetric theories. J. High Energ. Phys. 2014, 56 (2014). https://doi.org/10.1007/JHEP06(2014)056
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DOI: https://doi.org/10.1007/JHEP06(2014)056