Exact solutions of exceptional gauge theories from toric geometry Original Research Article

We derive four-dimensional gauge theories with the exceptional groups F4, E8, E7, and E7 with matter, by starting from the duality between the heterotic string on K3 and F-theory on a elliptically fibered Calabi-Yau 3-fold. This configuration is compactified to four dimensions 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 P1 base.