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 …

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 …

We consider a type III subfactor N⊂ N of finite index with a finite system of braided NN
morphisms which includes the irreducible constituents of the dual canonical endomorphism …

In this paper we further analyze modular invariants for subfactors, in particular the structure
of the chiral induced systems of MM morphisms. The relative braiding between the chiral …

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 …

Two-dimensional full conformal field theories have been studied in various mathematical
frameworks, from algebraic, operator-algebraic to categorical. In this work, we focus our …

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 …