A new vista on the heterotic moduli space from six and three dimensions

We settle a longstanding question about the hypermultiplet moduli spaces of the heterotic strings on asymptotically locally Euclidean 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 N=4 quiver gauge theories whose quantum corrected Coulomb branch coincides with the exact heterotic hypermultiplet moduli space.