An N=2 Superconformal Fixed Point with E_6 Global Symmetry

TL;DR

This paper constructs the elliptic curve and Seiberg-Witten differential for an N=2 superconformal field theory with E6 symmetry, analyzing its properties and implications for BPS masses in F-theory.

Contribution

It provides the explicit elliptic curve and Seiberg-Witten differential for an N=2 SCFT with E6 symmetry, including analysis of its reduction to D4 and monodromy computations.

Findings

Derived the elliptic curve for the E6 symmetric theory.

Identified the Seiberg-Witten differential with 27 poles.

Computed monodromies and BPS masses in F-theory.

Abstract

We obtain the elliptic curve corresponding to an $N=2$ superconformal field theory which has an $E_6$ global symmetry at the strong coupling point $\tau=e^{\pi i/3}$. We also find the Seiberg-Witten differential $\lambda_{SW}$ for this theory. This differential has 27 poles corresponding to the fundamental representation of $E_6$. The complex conjugate representation has its poles on the other sheet. We also show that the $E_6$ curve reduces to the $D_4$ curve of Seiberg and Witten. Finally, we compute the monodromies and use these to compute BPS masses in an $F$-Theory compactification.