Exceptional SW Geometry from ALE Fibrations

TL;DR

This paper demonstrates that the Seiberg-Witten curve for N=2 E6 Yang-Mills theory is equivalent to a fibration of the E6 ALE singularity, resolving a duality puzzle in string theory.

Contribution

It establishes a geometric equivalence between the Seiberg-Witten curve and ALE fibrations for E6, providing new insights into string dualities.

Findings

Seiberg-Witten curve matches ALE fibration geometry

Resolves a previously raised duality puzzle

Connects gauge theory curves with geometric singularities

Abstract

We show that the genus 34 Seiberg-Witten curve underlying $N=2$ Yang-Mills theory with gauge group $E_6$ yields physically equivalent results to the manifold obtained by fibration of the $E_6$ ALE singularity. This reconciles a puzzle raised by $N=2$ string duality.