A new vista on the Heterotic Moduli Space from Six and Three Dimensions

TL;DR

This paper determines the hypermultiplet moduli space of heterotic strings on ALE singularities using three-dimensional quiver gauge theories, resolving a longstanding question in string theory.

Contribution

It introduces a class of 3D $ abla$=4 quiver gauge theories whose Coulomb branches match the heterotic hypermultiplet moduli space, providing a new geometric perspective.

Findings

Exact heterotic hypermultiplet moduli space identified

Quantum corrected Coulomb branch matches the moduli space

Clarifies the role of singularity type and instanton number

Abstract

We settle a long-standing question about the hypermultiplet moduli spaces of the heterotic strings on ALE singularities. These heterotic backgrounds are specified by the singularity type, an instanton number, and a (nontrivial) flat connection at infinity. Building on their interpretation as six-dimensional theories, we determine a class of three-dimensional $\mathcal{N}=4$ quiver gauge theories whose quantum corrected Coulomb branch coincides with the exact heterotic hypermultiplet moduli space.