$E_9$ symmetry in the Heterotic String on $S^1$ and the Weak Gravity Conjecture

TL;DR

This paper demonstrates that heterotic string compactifications on a circle exhibit enhanced affine algebra symmetries at moduli space boundaries and confirms that associated mode towers satisfy the Weak Gravity and Repulsive Force Conjectures.

Contribution

It reveals the emergence of affine algebra symmetries in heterotic string compactifications and verifies the validity of the Weak Gravity and Repulsive Force Conjectures for these mode towers.

Findings

Enhanced affine algebra symmetries at moduli space boundaries

Towers of modes satisfy the Weak Gravity Conjecture

Towers of modes satisfy the Repulsive Force Conjecture

Abstract

We show that compactifications of the heterotic string on a circle exhibit at the boundary of moduli space ($R\to 0$, or equivalently the decompactification limit $R \to \infty$) a tower of winding or momentum modes that enhance the $E_8 \times E_8$ or $SO(32)$ gauge symmetry to the affine algebras $(E_9 \oplus E_9)/\sim$ (the identification means that the two copies of $E_9$ share the same central extension) and $\hat{D}_{16}$, respectively. We also prove that these towers of modes satisfy the lattice Weak Gravity and Repulsive Force Conjectures.