# Extensions of Conformal Nets¶and Superselection Structures

@article{Guido1998ExtensionsOC, title={Extensions of Conformal Nets¶and Superselection Structures }, author={Daniele Guido and Roberto Longo and Hans-Werner Wiesbrock}, journal={Communications in Mathematical Physics}, year={1998}, volume={192}, pages={217-244} }

Abstract:Starting with a conformal Quantum Field Theory on the real line, we show that the dual net is still conformal with respect to a new representation of the Möbius group. We infer from this that every conformal net is normal and conormal, namely the local von Neumann algebra associated with an interval coincides with its double relative commutant inside the local von Neumann algebra associated with any larger interval. The net and the dual net give together rise to an infinite dimensional… Expand

#### 102 Citations

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We consider conformal nets on $S^1$ of von Neumann algebras, acting on the full Fock space, arising in free probability. These models are twisted local, but non-local. We extend to the non-local case… Expand

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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 particular… Expand

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The subfactor theory provides a tool to analyze and construct extensions of Quantum Field Theories, once the latter are formulated as local nets of von Neumann algebras. We generalize some of the… Expand

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