  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.
