Affine algebras at infinite distance limits in the Heterotic String

We analyze the boundaries of the moduli spaces of compactifications of the heterotic string on T-d, making particular emphasis on d = 2 and its F-theory dual. We compute the OPE algebras as we approach all the infinite distance limits that correspond to (possibly partial) decompactification limits in some dual frame. When decompactifying k directions, we find infinite towers of states becoming light that enhance the algebra arising at a given point in the moduli space of the Td-k compactification to its k-loop version, where the central extensions are given by the k KK vectors. For T-2 compactifications, we reproduce all the affine algebras that arise in the F-theory dual, and show all the towers explicitly, including some that are not manifest in the F-theory counterparts. Furthermore, we construct the affine SO(32) algebra arising in the full decompactification limit, both in the heterotic and in the F-theory sides, showing that not only affine algebras of exceptional type arise in the latter.

Automated summary

This paper analyzes the boundaries of the moduli spaces of compactifications of the heterotic string on T-d, with a focus on d = 2 and its F-theory counterpart. The authors calculate the OPE algebras and study the infinite distance limits corresponding to decompactification limits in some dual frame. They find that when decompactifying k directions, there are infinite towers of states becoming light, enhancing the algebra at a given point in the moduli space. The article also investigates the affine algebras arising in T-2 compactifications and constructs the affine SO(32) algebra in the full decompactification limit.