Critical Phenomena, modular invariants and operator algebras

Abstract

We review the framework subfactors provide for understanding modular invariants. We discuss the structure of a generalized Longo-Rehren subfactor and the relationship between the coupling matrices of such subfactors, modular invariance and local extensions. We relate results of Kostant, in the context of the McKay correspondence for finite subgroups of SU(2), to subfactors. A direct proof of how alpha-induction produces modular invariants is presented.

27 pages

References in corpus (15)

• Modular Invariants, Graphs and $\alpha$-Induction for Nets of Subfactors. III
• Applications of braided endomorphisms from conformal inclusions
• Finite Group Modular Data
• Chiral structure of modular invariants for subfactors
• On $\alpha$-induction, chiral generators and modular invariants for subfactors
• From CFT's to Graphs
• Subfactor realisation of modular invariants
• Galois Modular Invariants of WZW Models
• WZW Commutants, Lattices, and Level 1 Partition Functions
• Solitonic sectors, alpha-induction and symmetry breaking boundaries
• An Algebraic Formulation of Level One Wess-Zumino-Witten Models
• Boundary conditions in charge conjugate sl(N) WZW theories
• Characterizing Invariants for Local Extensions of Current Algebras
• Subfactors and coset models
• Conformal field theory and graphs

Cited by in corpus (8)

• Subfactor realisation of modular invariants
• Ocneanu Cells and Boltzmann Weights for the SU(3) ADE Graphs
• The Nakayama automorphism of the almost Calabi-Yau algebras associated to SU(3) modular invariants
• Higher Coxeter graphs associated to affine su(3) modular invariants
• Spectral Measures and Generating Series for Nimrep Graphs in Subfactor Theory
• Modular Invariants and Twisted Equivariant K-theory II: Dynkin diagram symmetries
• Modular Invariants and Twisted Equivariant K-theory
• Braided Subfactors, Spectral Measures, Planar algebras and Calabi-Yau algebras associated to SU(3) modular invariants