A-D-E Classification of Conformal Field Theories

2009/11/17 by Andrea Cappelli, Cappelli, Andrea, Jean-Bernard Zuber +1 · 13 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Conformal map #Field (mathematics) #Geology #Geometry #Homotopy and Cohomology in Algebraic Topology #Mathematics #Nonlinear Waves and Solitons #Pure mathematics

paper · pdf · doi:10.4249/scholarpedia.10314

published in Scholarpedia 5(4), 10314 (Scholarpedia Corporation)

openalex publication_date 2010/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

The ADE classification scheme is encountered in many areas of mathemat-ics, most notably in the study of Lie algebras. Here such a scheme is shown to describe families of two-dimensional conformal field theories. Review article to appear in Scholapedia,

Citations

• Infinite conformal symmetry in two-dimensional quantum field theory
• On the construction of integrable dilute ADE models
• Non-Abelian anyons and topological quantum computation

Cited by

• Partition functions of non-Abelian quantum Hall states
• Defects and perturbation
• Generalised 4d Partition Functions and Modular Differential Equations
• ADE triality via (non-)invertible symmetry gauging
• Cellular automaton [wikipedia]

Related

• Classification of operator algebraic conformal field theories in dimensions one and two
• Conformal Field Theory in D>2 dimensions, representations and harmonic analysis
• Notes on 2D Conformal Field Theory and String Theory
• Applied Conformal Field Theory
• Algebraic Structures in Euclidean and Minkowskian Two-Dimensional Conformal Field Theory