Linear Sigma Models for the R^8/Z_k Orbifold

TL;DR

This paper constructs N=4 gauged linear sigma models in two dimensions with Higgs branches that are R^8/Z_k orbifolds or their generalizations, featuring hyperKahler 8-manifolds of ALF or ALE type.

Contribution

It introduces new linear sigma models with specific hyperKahler geometries and a quiver diagram structure for the ALE case, expanding the understanding of orbifold singularities.

Findings

Higgs branches include R^8/Z_k orbifolds and their generalizations.

Models feature hyperKahler 8-manifolds of ALF or ALE type.

Quiver diagram specifies matter content for ALE models.

Abstract

We construct N=4 gauged linear sigma models in two dimensions whose Higgs branch has a R^8/Z_k orbifold singularity or its generalization. Our linear sigma models have either ALF or ALE type hyperKahler 8-manifolds as their Higgs branch. For the ALE case, the matter content of our model is specified by a quiver diagram which is a union of two A-type extended Dynkin diagrams overlapping at one link.