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Communications in Mathematical Physics

, Volume 192, Issue 1, pp 217–244 | Cite as

Extensions of Conformal Nets¶and Superselection Structures

  • D. Guido
  • R. Longo
  • H.-W. Wiesbrock

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 symmetry group, of which we study a class of positive energy irreducible representations. We mention how superselection sectors extend to the dual net and we illustrate by examples how, in general, this process generates solitonic sectors. We describe the free theories associated with the lowest weight n representations of \(\), showing that they violate 3-regularity for $n > 2. When n≥ 2, we obtain examples of non Möbius-covariant sectors of a 3-regular (non 4-regular) net.

Keywords

Symmetry Group Irreducible Representation Real Line Relative Commutant Lower Weight 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • D. Guido
    • 1
  • R. Longo
    • 1
  • H.-W. Wiesbrock
    • 2
  1. 1.Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica, I–00133 Roma, Italy. E-mail: guido@mat.utovrm.it, longo@mat.utovrm.itIT
  2. 2.Freie Universität Berlin, Institut für Theoretische Physik, Arnimallee 14, D-14195 Berlin, Germany.¶E-mail: wiesbroc@physik.fu-berlin.deDE

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