The Higgs branch of Heterotic ALE instantons

TL;DR

This paper explores the Higgs branch of six-dimensional heterotic little string theories on ALE spaces by constructing magnetic quivers, providing new insights into instanton transitions and their gauge theory descriptions.

Contribution

It introduces a magnetic quiver framework for the Higgs branch of heterotic ALE instantons, including small instanton transitions, for both $SO(32)$ and $E_8 imes E_8$ heterotic strings.

Findings

Constructed magnetic quivers for heterotic ALE instantons.

Analyzed small instanton transitions via magnetic quivers.

Validated the approach for $ ext{ALE}$ spaces and different heterotic string types.

Abstract

We begin a study of the Higgs branch of six-dimensional $(1,0)$ little string theories governing the worldvolumes of heterotic ALE instantons. We give a description of this space by constructing the corresponding magnetic quiver. The latter is a three-dimensional $\mathcal{N}=4$ quiver gauge theory that flows in the infrared to a fixed point whose quantum corrected Coulomb branches is the Higgs branch of the six-dimensional theory of interest. We present results for both types of heterotic strings, and mostly for $\mathbb C^2/\mathbb Z_k$ ALE spaces. Our analysis is valid both in the absence and in the presence of small instantons. Along the way, we also describe small $SO(32)$ instanton transitions in terms of the corresponding magnetic quiver, which parallels a similar treatment of the small $E_8$ instanton transitions in the context of the $E_8\times E_8$ heterotic string.