1998/10/31 by Feng Xu · 1 citation
Mathematics · Physics and Astronomy · #Algebraic number #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Conformal field theory #Conformal map #Conjecture #Coset #Field (mathematics) #Fusion rules #Homotopy and Cohomology in Algebraic Topology #Primary field #Unitary state #math-ph #math.MP #math.OA #math.QA
paper · pdf · doi:10.1007/s002200050800
published as Commun.Math.Phys. 211 (2000) 1-43 · 49 pages, Improved presentations and added details, to appear in Comm.Math.Phys
arxiv created 2000/02/29 · openalex publication_date 2000/04/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
All unitary Rational Conformal Field Theories (RCFT) are conjectured to be related to unitary coset Conformal Field Theories, i.e., gauged Wess-Zumino-Witten (WZW) models with compact gauge groups. In this paper we use subfactor theory and ideas of algebraic quantum field theory to approach coset Conformal Field Theories. Two conjectures are formulated and their consequences are discussed. Some results are presented which prove the conjectures in special cases. In particular, one of the results states that a class of representations of coset WN (N≥ 3) algebras with critical parameters are irreducible, and under the natural compositions (Connes' fusion), they generate a finite dimensional fusion ring whose structure constants are completely determined, thus proving a long-standing conjecture about the representations of these algebras.