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

Abstract

We show that compactifications of the heterotic string on a circle exhibit at the boundary of moduli space (R → 0, or equivalently the decompactification limit R → ∞) a tower of winding or momentum modes that enhance the E 8 × E 8 or SO(32) gauge symmetry to the affine algebras (E 9 ⊕ E 9 )/ ∼ (the identification means that the two copies of E 9 share the same central extension) and D16 , respectively. We also prove that these towers of modes satisfy the lattice weak gravity and repulsive force conjectures.