2021/07/31 by Justin Kaidi, Ying-Hsuan Lin, Julio Parra-Martinez
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebra over a field #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Computer science #Conformal field theory #Conformal map #Differential (mechanical device) #Holomorphic function #Mathematical analysis #Mathematics #Modular design #Modular form #Physics #Pure mathematics #Representation (politics) #Set (abstract data type) #Wronskian #hep-th #math.NT #math.QA
paper · pdf · doi:10.1007/jhep12(2021)151
39+15 pages, 14 tables; v2: minor revision
arxiv created 2021/08/17 · openalex publication_date 2021/12/01 · arxiv updated 2022/01/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A bstract In this work we revisit the “holomorphic modular bootstrap”, i.e. the classification of rational conformal field theories via an analysis of the modular differential equations satisfied by their characters. By making use of the representation theory of PSL(2 , ℤ n ), we describe a method to classify allowed central charges and weights ( c, h i ) for theories with any number of characters d . This allows us to avoid various bottlenecks encountered previously in the literature, and leads to a classification of consistent characters up to d = 5 whose modular differential equations are uniquely fixed in terms of ( c, h i ). In the process, we identify the full set of constraints on the allowed values of the Wronskian index for fixed d ≤ 5.