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A subtheory of a quantum field theory specifies von Neumann subalgebras $\mathcal{A(O)}$ (the ‘observables’ in the space-time region ${\mathcal O}$) of the von Neumann algebras $\mathcal{B(O)}$ (the… (More)

We prove the equality between the statistics phase and the conformal univalence for a superselection sector with finite index in Conformal Quantum Field Theory onS1. A relevant point is the… (More)

Making use of a recent result of Borchers, an algebraic version of the Bisognano-Wichmann theorem is given for conformal quantum field theories, i.e. the Tomita-Takesaki modular group associated with… (More)

- Roberto Longo
- 1994

We provide a duality between subfactors with finite index, or finite dimensional semisimple Hopf algebras, and a class ofC*-categories of endomorphisms.

Let $M$ be a factor with separable predual and $G$ a compact group of automorphisms of $M$ whose action is minimal, i.e. $M^{G^\prime}\cap M = C$, where $M^G$ denotes the $G$-fixed point subalgebra.… (More)

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 with the pairs… (More)

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 with the pairs… (More)

Abstract Given two von Neumann algebras A ⊂ B we study the relation between the existence of an interpolating type I factor F , namely A ⊂ F ⊂ B , the implementability of the flip automorphism of A ⊗… (More)

- Roberto Longo
- 2003

Abstract: Given an irreducible local conformal net 𝒜 of von Neumann algebras on S1 and a finite-index conformal subnet ℬ⊂𝒜, we show that 𝒜 is completely rational iff ℬ is completely rational. In… (More)

- Roberto Longo
- 2001

Abstract: We view DHR superselection sectors with finite statistics as Quantum Field Theory analogs of elliptic operators where KMS functionals play the role of the trace composed with the heat… (More)