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

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 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.

18 pages, 10 figures; v2: additional references and minor changes; published version

References in corpus (4)

• Tinkertoys for Gaiotto Duality
• Comments on scaling limits of 4d N=2 theories
• Hilbert Series for Moduli Spaces of Instantons on C^2/Z_n
• N=2 SU Quiver with USP Ends or SU Ends with Antisymmetric Matter

Cited by in corpus (8)

• $E_8$ instantons on type-A ALE spaces and supersymmetric field theories
• 5d fixed points from brane webs and O7-planes
• The moduli space of instantons on an ALE space from 3d $\mathcal{N}=4$ field theories
• Brane webs in the presence of an $O{5}^{-}$-plane and 4d class S theories of type D
• Anyonic Defect Branes and Conformal Blocks in Twisted Equivariant Differential (TED) K-theory
• Aspects of the moduli space of instantons on $\mathbb{C}{P}^2$ and its orbifolds
• The ADHM-like Constructions for Instantons on CP^2 and Three Dimensional Gauge Theories
• Instantons and Bows for the Classical Groups