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

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

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