2000/08/07 by J. Böckenhauer, David Evans, Böckenhauer, J. +2
Mathematics · Physics and Astronomy · #18D10 (Secondary) #22E67 #46L60 #81R10 #81T05 #81T40 (Primary) 46L37 #82B23 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Operator Algebras (math.OA) #Quantum Algebra (math.QA) #math-ph #math.MP #math.OA #math.QA #msc:18D10 #msc:22E67 #msc:46L37 #msc:46L60 #msc:81R10 #msc:81T05 #msc:81T40 #msc:82B23
paper · pdf · doi:10.48550/arxiv.math/0008056
25 pages, AMS LaTeX, epic, eepic, doc-class fic-1.cls
arxiv created 2000/08/07 · openalex publication_date 2000/08/07 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
In this lecture we explain the intimate relationship between modular invariants in conformal field theory and braided subfactors in operator algebras. Our analysis is based on an approach to modular invariants using braided sector induction ("α-induction") arising from the treatment of conformal field theory in the Doplicher-Haag-Roberts framework. Many properties of modular invariants which have so far been noticed empirically and considered mysterious can be rigorously derived in a very general setting in the subfactor context. For example, the connection between modular invariants and graphs (cf. the A-D-E classification for SU(2)k) finds a natural explanation and interpretation. We try to give an overview on the current state of affairs concerning the expected equivalence between the classifications of braided subfactors and modular invariant two-dimensional conformal field theories.