Skip to main content
Log in

Extensions of Conformal Nets¶and Superselection Structures

  • Published:
Communications in Mathematical Physics Aims and scope Submit manuscript


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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

Author information

Authors and Affiliations


Additional information

Received: 19 March 1997 / Accepted: 1 July 1997

Rights and permissions

Reprints and permissions

About this article

Cite this article

Guido, D., Longo, R. & Wiesbrock, HW. Extensions of Conformal Nets¶and Superselection Structures . Comm Math Phys 192, 217–244 (1998).

Download citation

  • Issue Date:

  • DOI: