EXACT-SOLUTIONS OF EXCEPTIONAL GAUGE-THEORIES FROM TORIC GEOMETRY

We derive four-dimensional gauge theories with the exceptional groups F-4, E-8, E-7, and E-7 with matter, by starting from the duality betwe en the heterotic string on K3 and F-theory on a elliptically fibered C alabi-Yau 3-fold. This configuration is compactified to four dimension s on a torus, and by employing toric geometry, we compute the type IIB mirrors of the Calabi-Yaus of the type IIA string theory. We identify the Seiberg-Witten curves describing the gauge theories as ALE spaces fibered over a P-1 base. (C) 1997 Elsevier Science B.V.