Exceptional Seiberg-Witten Geometry with Massive Fundamental Matters

TL;DR

This paper develops a Seiberg-Witten geometric framework for N=2 gauge theories with gauge group E6 and massive fundamental hypermultiplets, revealing complex mass-dependent fibering structures.

Contribution

It introduces a novel Seiberg-Witten geometry for E6 gauge theories with massive matter, detailing the intricate mass dependence of the fibering data over the base.

Findings

Describes the manifold as a fibration of E6 ALE space

Shows the fibering data depends intricately on hypermultiplet masses

Provides a geometric understanding of mass effects in E6 gauge theories

Abstract

We propose Seiberg-Witten geometry for N=2 gauge theory with gauge group $E_6$ with massive $N_f$ fundamental hypermultiplets. The relevant manifold is described as a fibration of the ALE space of $E_6$ type. It is observed that the fibering data over the base ${\bf CP}^1$ has an intricate dependence on hypermultiplet bare masses.