Hypermultiplet Moduli Space and Three Dimensional Gauge Theories

TL;DR

This paper proves a conjecture linking the hypermultiplet moduli space in heterotic string compactifications with A-D-E singularities to the moduli space of three-dimensional pure gauge theories, including effects of heterotic fivebranes.

Contribution

It establishes a precise relation between string theory moduli spaces and three-dimensional gauge theory moduli spaces, extending previous conjectures.

Findings

Hypermultiplet moduli space corresponds to 3D gauge theory moduli space.

Inclusion of heterotic fivebranes is consistent with perturbative string theory.

The relation holds in the leading order of lpha'.

Abstract

We establish a relation, conjectured recently by E. Witten, between the hypermultiplet moduli space in compactifications of the heterotic string on an A-D-E singularities, and the moduli spaces of three dimensional pure gauge theories with the corresponding A-D-E gauge groups. It is possible to add a bounded number of heterotic fivebranes sitting in the singularity, while (in leading order in $\alpha'$) keeping the heterotic string perturbative. The corresponding hypermultiplet moduli space is given by the moduli space of a three dimensional gauge theory with matter.