Affine algebras at infinite distance limits in the Heterotic String

• Published in: The journal of high energy physics 2023-07, Vol.2023 (7), p.36-49, Article 36
• Main Authors: Collazuol, Veronica, Graña, Mariana, Herráez, Alvaro, De Freitas, Héctor Parra
• Format: Article
• Language: English
• Subjects: Algebra; Classical and Quantum Gravitation; Elementary Particles; F-Theory; Gauge Symmetry; High energy physics; High Energy Physics - Theory; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; String Duality; String Theory; Strings; Superstrings and Heterotic Strings; Symmetry; Topological manifolds; Towers
• ISSN: 1029-8479; 1126-6708; 1029-8479
• DOI: 10.1007/JHEP07(2023)036

A bstract 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.