2013/10/07 by Liang Kong, Qin Li, Ingo Runkel
Mathematics · Physics and Astronomy · #Algebra over a field #Algebraic structures and combinatorial models #Axiom #Computer science #Conformal map #Field (mathematics) #Genus #Geometry #Homotopy and Cohomology in Algebraic Topology #Mathematical analysis #Mathematics #Modular design #Modular invariance #Nonlinear Waves and Solitons #Pure mathematics #Transformation (genetics) #hep-th #math.CT #math.QA
paper · pdf · doi:10.1016/j.aim.2014.05.020
published as Advances in Mathematics 262 (2014) 604-681 · 79 pages, 244 figures, comments are welcome
arxiv created 2013/10/07 · openalex publication_date 2014/06/12 · arxiv updated 2014/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
This is the part II of a two-part work started in arXiv:0807.3356 [math.QA]. In part I, Cardy algebras were studied, a notion which arises from the classification of genus-0,1 open-closed rational conformal field theories. In this part, we prove that a Cardy algebra also satisfies the higher genus factorisation and modular-invariance properties formulated in arXiv:hep-th/0612306 in terms of the notion of a solution to the sewing constraints. We present the proof by showing that the latter notion, which is defined as a monoidal natural transformation, can be expressed in terms of generators and relations, which correspond exactly to the defining data and axioms of a Cardy algebra.