Affine algebras at infinite distance limits in the Heterotic String

Abstract

Abstract 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 T d−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.

Keywords

• F-Theory
• Gauge Symmetry
• String Duality
• Superstrings and Heterotic Strings