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Sfb 288 Differential Geometry and Quantum Physics |
Abstract for Sfb Preprint No. 255
Extensions of Conformal Nets and Superselection Structures D. Guido, R. Longo, H.-W. Wiesbrock
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 M"obius 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 $PSL(2R)/Z_2$, showing that they violate 3-regularity for $n>2$. When $ngeq2$, we obtain examples of non M"obius-covariant sectors of a 3-regular (non 4-regular) net
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