N=1 M-theory-Heterotic Duality in Three Dimensions and Joyce Manifolds
  It is argued that $M$-theory compactified on {\it any} of Joyce's $Spin(7)$ holonomy 8-manifolds are dual to compactifications of heterotic string theory on Joyce 7-manifolds of $G_2$ holonomy. 
B.S.Acharya (Queen Mary and Westfield College, London.)