Conformal nets IV: The 3-category

Arthur Bartels, Christopher L. Douglas, André Henriques

Research output: Contribution to journalArticleProfessional


Conformal nets are a mathematical model for conformal field theory, and defects between conformal nets are a model for an interaction or phase transition between two conformal field theories. We previously introduced a notion of composition, called fusion, between defects. We also described a notion of sectors between defects, modeling an interaction among or transformation between phase transitions, and defined fusion composition operations for sectors. In this paper we prove that altogether the collection of conformal nets, defects, sectors, and intertwiners, equipped with the fusion of defects and fusion of sectors, forms a symmetric monoidal 3-category. This 3-category encodes the algebraic structure of the possible interactions among conformal field theories.

Original languageEnglish
Pages (from-to)897-956
Number of pages60
JournalAlgebraic and Geometric Topology
Issue number2
Publication statusPublished - 12 Mar 2018


  • 3-category
  • Conformal field theory
  • Conformal net
  • Connes fusion
  • Defect
  • Fusion
  • Sector
  • Topological field theory
  • Von neumann algebra


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