A Non-Perturbative Superpotential With $E_8$ Symmetry

TL;DR

This paper calculates a non-perturbative superpotential in F-theory compactifications, revealing that it exhibits modular properties and is represented by an E8 theta function, highlighting a novel connection between geometry and symmetry.

Contribution

It introduces a new class of superpotentials with E8 symmetry in F-theory, demonstrating their modular properties and explicit theta function form.

Findings

Superpotential has E8 theta function structure

Reveals modular properties in F-theory superpotentials

Connects geometric compactification data with E8 symmetry

Abstract

We compute the non-perturbative superpotential in $F$-theory compactification to four dimensions on a complex three-fold $\P^1\times S$, where $S$ is a rational elliptic surface. In contrast to examples considered previously, the superpotential in this case has interesting modular properties; it is essentially an $E_8$ theta function.