Conformal nets IV: The 3-category

Understand

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.

• In the preceding paper of this series, we 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.