State counting on fibered CY 3-folds and the non-Abelian weak gravity conjecture

• Published in: The journal of high energy physics 2021-05, Vol.2021 (5), p.1-77, Article 30
• Main Authors: Cota, Cesar Fierro, Klemm, Albrecht, Schimannek, Thorsten
• Format: Article
• Language: English
• Subjects: Black holes; Classical and Quantum Gravitation; Elementary Particles; F-Theory; Geometry; Gravity; High energy physics; Homology; Isomorphism; M theory; Mathematics; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; String Theory; Strings; Superstrings and Heterotic Strings; Topological Strings
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP05(2021)030

A bstract We extend the dictionary between the BPS spectrum of Heterotic strings and the one of F-/M-theory compactifications on K 3 fibered Calabi-Yau 3-folds to cases with higher rank non-Abelian gauge groups and in particular to dual pairs between Heterotic CHL orbifolds and compactifications on Calabi-Yau 3-folds with a compatible genus one fibration. We show how to obtain the new supersymmetric index purely from the Calabi-Yau geometry by reconstructing the Noether-Lefschetz generators, which are vector-valued modular forms. There is an isomorphism between the latter objects and vector-valued lattice Jacobi forms, which relates them to the elliptic genera and twisted-twined elliptic genera of six- and five-dimensional Heterotic strings. The meromorphic Jacobi forms generate the dimensions of the refined cohomology of the Hilbert schemes of symmetric products of the fiber and allow us to refine the BPS indices in the fiber and therefore to obtain, conjecturally, actual state counts. Using the properties of the vector-valued lattice Jacobi forms we also provide a mathematical proof of the non-Abelian weak gravity conjecture for F-/M-theory compactified on this general class of fibered Calabi-Yau 3-folds.