Geometry and N=2 Exceptional Gauge Theories

TL;DR

This paper derives the Seiberg-Witten geometries for four-dimensional N=2 supersymmetric E_6 and E_7 gauge theories with fundamental hypermultiplets by embedding them into type II string theories on Calabi-Yau threefolds, confirming recent results.

Contribution

It provides a geometric derivation of Seiberg-Witten geometries for E_6 and E_7 gauge theories, extending previous work to include massive hypermultiplets.

Findings

Seiberg-Witten geometry for E_6 with massless hypermultiplets

Seiberg-Witten geometry for E_7 with massive hypermultiplets

Geometric embedding in type II string theories on Calabi-Yau threefolds

Abstract

We find the Seiberg-Witten geometry for four dimensional N=2 supersymmetric E_6 gauge theories with massless fundamental hypermultiplets, by geometrically embedding them in type II string theories compactified on Calabi-Yau threefolds. The resulting geometry completely agrees with that of recent works, which are based on the technique of N=1 confining phase superpotentials. We also derive the Seiberg-Witten geometry for E_7 gauge theories with massive fundamental hypermultiplets.