As an application of the general theory established in the first part, we determine the
structure of Longo–Rehren inclusions for several systems of sectors arising from …

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We review the physical meaning of modular invariance for unitary conformal quantum field
theories in d= 2. For quantum field theory models, while T invariance is necessary for …

A bstract This is the first part of a two-part work on a unified mathematical theory of gapped
and gapless edges of 2d topological orders. We analyze all the possible observables on the …

We completely classify diffeomorphism covariant local nets of von Neumann algebras on the
circle with central charge c less than 1. The irreducible ones are in bijective correspondence …

C* tensor categories are a point of contact where Operator Algebras and Quantum Field
Theory meet. They are the underlying unifying concept for homomorphisms of (properly …

We continue to develop the theory of separable higher categories, including center functors,
higher centralizers, modular extensions and group theoretical higher fusion categories …

In this work, we give a mathematical description of a chiral gapless edge of a 2d topological
order (without symmetry). We show that the observables on the 1+ 1D world sheet of such …

Conformal quantum field theory on the half-space x> 0 of Minkowski space-time (" boundary
CFT") is analyzed from an algebraic point of view, clarifying in particular the algebraic …

Given an irreducible local conformal net 𝒜 of von Neumann algebras on S 1 and a finite-
index conformal subnet ℬ⊂ 𝒜, we show that 𝒜 is completely rational iff ℬ is completely …