Extensions of Conformal Netsand Superselection Structures
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 3regularity for $n > 2. When n>= 2, we obtain examples of non Möbiuscovariant sectors of a 3regular (non 4regular) net.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 1998
 DOI:
 10.1007/s002200050297
 arXiv:
 arXiv:hepth/9703129
 Bibcode:
 1998CMaPh.192..217G
 Keywords:

 High Energy Physics  Theory;
 Mathematics  Functional Analysis
 EPrint:
 34 pages, Latex2e. Some points have been clarified and some references have been added. To appear in Communications in Mathematical Physics