Hypermultiplet moduli space and three dimensional gauge theories

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 α') keeping the heterotic string perturbative. The corresponding hypermultiplet moduli space is given by the moduli space of a three-dimensional gauge theory with matter.