String-string dualities in D=6,4 dimensions

We study heterotic E(8) x E(8) models that are dual to compactifications of F-theory and type IIA string on certain classes of elliptically fibered Calabi-Yau manifolds. Different choices for the specific torus in the fibration have heterotic duals that are most easily understood in terms of Ee x Es models with gauge backgrounds of type H x U(1)(8-d), where H is a non-Abelian factor. The case with d = 8 corresponds to the well known E(8) x E(8) compactifications with non-Abelian instanton backgrounds (k(1),k(2)) whose F-theory duals are built through compactifications on fibrations of the torus P-2((1,2,3))[6] over F-n. The new cases with d < 8 correspond to other choices for the elliptic fiber over the same base and yield unbroken U(1)'s, some of which are anomalous and acquire a mass by swallowing zero modes of the antisymmetric B-MN field. We also study transitions to models with no tensor multiplets in D = 6 and find evidence of E(d) instanton dynamics.