Exact Solutions of Exceptional Gauge Theories from Toric Geometry

Details Exact Solutions of Exceptional Gauge Theories from Toric Geometry Exact Solutions of Exceptional Gauge Theories from Toric Geometry

1997-05-11

arxiv.org/abs/hep-th/9705068v1

Nucl.Phys. B506 (1997) 183-198

Physics

High Energy Physics

High Energy Physics - Theory

18 pages, 5 figures, uses harvmac and epsf

Scientific paper

10.1016/S0550-3213(97)00523-3

We derive four dimensional gauge theories with exceptional groups $F_4$, $E_8$, $E_7$, and $E_7$ 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 $P^1$ base.

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