STRING-STRING DUALITIES IN D=6,4 DIMENSIONS

We study heterotic E(8) x E(8) models that are dual to compactificatio ns 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 t o the well known E(8) x E(8) compactifications with non-Abelian instan ton backgrounds (k(1),k(2)) whose F-theory duals are built through com pactifications on fibrations of the torus P-2((1,2,3))[6] over F-n. Th e new cases with d < 8 correspond to other choices for the elliptic fi ber over the same base and yield unbroken U(1)'s, some of which are an omalous and acquire a mass by swallowing zero modes of the antisymmetr ic B-MN field. We also study transitions to models with no tensor mult iplets in D = 6 and find evidence of E(d) instanton dynamics.