E9 symmetry in the heterotic string on S1 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 E8×E8 or SO(32) gauge symmetry to the affine algebras (E9 ⊕ E9)/ ∼ (the identification means that the two copies of E9 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.