Superconformal Fixed Points with E_n Global Symmetry

TL;DR

This paper constructs the Seiberg-Witten solution for an N=2 superconformal field theory with E8 symmetry, revealing new features in the differential and its implications for related theories with lower symmetries.

Contribution

It provides the elliptic curve and Seiberg-Witten differential for an E8 symmetric superconformal theory at strong coupling, introducing a novel lambda_{SW} based on adjoint representations.

Findings

Derived the elliptic curve and differential with 120 poles

Connected the E8 theory to E7, E6, and D4 flows

Identified differences in physics based on representation choices

Abstract

We obtain the elliptic curve and the Seiberg-Witten differential for an $N=2$ superconformal field theory which has an $E_8$ global symmetry at the strong coupling point $\tau=e^{\pi i/3}$. The differential has 120 poles corresponding to half the charged states in the fundamental representation of $E_8$, with the other half living on the other sheet. Using this theory, we flow down to $E_7$, $E_6$ and $D_4$. A new feature is a $\lambda_{SW}$ for these theories based on their adjoint representations. We argue that these theories have different physics than those with $\lambda_{SW}$ built from the fundamental representations.