Exact Solutions of Exceptional Gauge Theories from Toric Geometry

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.

18 pages, 5 figures, uses harvmac and epsf

Cited by in corpus (6)

• Classification of 4d N=2 gauge theories
• Seiberg-Witten Geometries Revisited
• String Dualities and Toric Geometry: An Introduction
• Rigid Limit in N=2 Supergravity and Weak-Gravity Conjecture
• Exact solutions for some N=2 supersymmetric SO(N) gauge theories with vectors and spinors
• Exceptional Seiberg-Witten Geometry with Massive Fundamental Matters