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arXiv · 1402.4200

Moduli spaces of SO(8) instantons on smooth ALE spaces as Higgs branches of 4d N=2 supersymmetric theories

Yuji Tachikawa
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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 x 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 hyperk\"ahler 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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Yuji Tachikawa. 2014-02-18. Moduli spaces of SO(8) instantons on smooth ALE spaces as Higgs branches of 4d N=2 supersymmetric theories. https://doi.org/10.1007/jhep06(2014)056

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