Bootstrapping fermionic rational CFTs with three characters

• Published in: The journal of high energy physics 2022-01, Vol.2022 (1), p.1-60, Article 89
• Main Authors: Bae, Jin-Beom, Duan, Zhihao, Lee, Kimyeong, Lee, Sungjay, Sarkis, Matthieu
• Format: Article
• Language: English
• Subjects: Algebra; Classical and Quantum Gravitation; Classification; Conformal Field Theory; Differential equations; Elementary Particles; Fermions; Field Theories in Lower Dimensions; High energy physics; Physics; Physics and Astronomy; Poles; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; String Theory; Subgroups
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP01(2022)089

A bstract Recently, the modular linear differential equation (MLDE) for level-two congruence subgroups Γ θ , Γ 0 (2) and Γ 0 (2) of SL 2 (ℤ) was developed and used to classify the fermionic rational conformal field theories (RCFT). Two character solutions of the second-order fermionic MLDE without poles were found and their corresponding CFTs are identified. Here we extend this analysis to explore the landscape of three character fermionic RCFTs obtained from the third-order fermionic MLDE without poles. Especially, we focus on a class of the fermionic RCFTs whose Neveu-Schwarz sector vacuum character has no free-fermion currents and Ramond sector saturates the bound h R ≥ C 24 , which is the unitarity bound for the supersymmetric case. Most of the solutions can be mapped to characters of the fermionized WZW models. We find the pairs of fermionic CFTs whose characters can be combined to produce K ( τ ), the character of the c = 12 fermionic CFT for Co 0 sporadic group.