Conformal field theory, tensor categories and operator algebras

2015/03/31 by Yasuyuki Kawahigashi
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebra over a field #Algebra representation #Algebraic structures and combinatorial models #Compact operator #Computer science #Conformal field theory #Conformal map #Field (mathematics) #Jordan algebra #Ladder operator #Mathematical analysis #Mathematical physics #Mathematics #Operator (biology) #Operator algebra #Operator product expansion #Primary field #Pure mathematics #Representation theory #Shift operator #Vertex operator algebra #hep-th #math-ph #math.MP #math.OA #math.QA

paper · pdf · doi:10.1088/1751-8113/48/30/303001

published as J. Phys. A 48 (2015), 303001 · Lectures notes, 66 pages: references and explanations added, typos fixed

openalex publication_date 2015/07/10 · arxiv created 2018/04/23 · arxiv updated 2018/04/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

This is a set of lecture notes on the operator algebraic approach to 2-dimensional conformal field theory. Representation theoretic aspects and connections to vertex operator algebras are emphasized. No knowledge on operator algebras or quantum field theory is assumed.

Citations

• Operator algebras and conformal field theory
• Exotic Subfactors of Finite Depth with Jones Indices (5+√(13))/2 and (5+√(17))/2
• Algebraic Coset Conformal Field Theories
• On the Representation Theory of Virasoro Nets
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• Integrating Unitary Representations of Infinite-Dimensional Lie Groups
• Monstrous moonshine and monstrous Lie superalgebras
• Invariants of 3-manifolds via link polynomials and quantum groups
• Classification of amenable subfactors of type II
• The friendly giant
• TFT construction of RCFT correlators II: unoriented world sheets
• Meromorphicc=24 conformal field theories
• RIGIDITY AND MODULARITY OF VERTEX TENSOR CATEGORIES
• Duality and defects in rational conformal field theory
• Modular structure and duality in conformal quantum field theory
• The Classification of Non-Local Chiral CFT with c < 1
• TFT construction of RCFT correlators I: partition functions
• Classification of Injective Factors Cases II 1 , II ∞ , III λ , λ � 1
• Monstrous Moonshine
• Sphere Packings, Lattices and Groups