N=1 Heterotic-Supergravity Duality and Joyce Manifolds

We construct the heterotic dual theory in four dimensions of eleven dimensional supergravity compactified on a particular Joyce manifold, $J$. In particular, $J$ is constructed from resolving fixed point singularities of orbifolds of the seven torus in such a way that one is forced to consider a generalised orbifold on the heterotic side. We conjecture that a heterotic dual exists for all the compact 7-manifolds of $G_{2}$ holonomy constructed by Joyce.