Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1997-03-18
Commun.Math.Phys.192:217-244,1998
Physics
High Energy Physics
High Energy Physics - Theory
34 pages, Latex2e. Some points have been clarified and some references have been added. To appear in Communications in Mathema
Scientific paper
10.1007/s002200050297
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 Moebius 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 superselsection 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 PSL(2,R), showing that they violate 3-regularity for n>2. When n>1, we obtain examples of non Moebius-covariant sectors of a 3-regular (non 4-regular) net.
Guido Daniele
Longo Roberto
Wiesbrock Hans-Werner
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