Exact Solutions of Exceptional Gauge Theories from Toric Geometry

TL;DR

This paper constructs exact four-dimensional gauge theories with exceptional groups using dualities and toric geometry, providing explicit Seiberg-Witten solutions for these theories.

Contribution

It introduces a novel method to derive exceptional gauge theories from string dualities and toric geometry, including explicit Seiberg-Witten curves.

Findings

Derived gauge theories with $F_4$, $E_8$, $E_7$ groups from string dualities.

Computed mirror geometries using toric methods.

Identified Seiberg-Witten curves as ALE spaces fibered over $P^1$.

Abstract

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.