$E_9$ 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 ($R\to 0$, 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.

27 pages, 3 tables, 1 figure

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