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
Multi-Interval Subfactors and Modularity¶of Representations in Conformal Field Theory
Abstract: We describe the structure of the inclusions of factors ?(E)⊂?(E′)′ associated with multi-intervals E⊂ℝ for a local irreducible net ? of von Neumann algebras on the real line satisfying theExpand
Topological Sectors and a Dichotomy in Conformal Field Theory
Let be a local conformal net of factors on S1 with the split property. We provide a topological construction of soliton representations of the n-fold tensor product that restrict to trueExpand
On the Uniqueness of Diffeomorphism Symmetry in Conformal Field Theory
A Möbius covariant net of von Neumann algebras on S1 is diffeomorphism covariant if its Möbius symmetry extends to diffeomorphism symmetry. We prove that in case the net is either a Virasoro net orExpand
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Conformal Nets, Maximal Temperature and Models from Free Probability
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Infinite index extensions of local nets and defects
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 theExpand
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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 pairsExpand
Classification of local conformal nets
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 pairsExpand
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