Hyperbolization of Affine Lie Algebras

Kaiwen Sun, University of Science and Technology of China, Hefei, People's Republic of China. Haowu Wang, Wuhan University, People's Republic of China. Brandon Williams, Heidelberg University, Germany

Chapters; 1. Introduction; 2. Preliminaries; 3. The hyperbolization of affine Kac-Moody algebras; 4. Root systems associated with reflective Borcherds products of singular weight; 5. The classification of affine Lie algebras with hyperbolizations; 6. The antisymmetric case: holomorphic CFTs of central charge 24; 7. The symmetric case: holomorphic SCFTs of central charge 12; 8. The symmetric case: four exotic CFTs; 9. The 12 symmetric cases: the construction as additive lifts; 10. Fourier expansions of singular-weight reflective Borcherds products; 11. The classification of anti-symmetric root systems; 12. The classification of symmetric root systems; 13. Application: anti-symmetric Siegel paramodular forms of weight 3; 14. Remarks, questions and conjectures; 15. Long tables