Massless Wigner particles in conformal field theory are free

We show that in a four dimensional conformal Haag-Kastler net, its massless particle spectrum is generated by a free field subnet. If the massless particle spectrum is scalar, then the free field subnet decouples as a tensor product component.Comment: 25 pages, 3 Tikz figures. The final version is available under Open Acces

Ground state representations of some non-rational conformal nets

We construct families of ground state representations of the U(1)-current net and of the Virasoro nets Vir_c with central charge c >= 1. We show that these representations are not covariant with respect to the original dilations, and those on the U(1)-current net are not solitonic. Furthermore, by going to the dual net with respect to the ground state representations of Vir_c, we obtain a possibly new family of M\"obius covariant nets on S^1.Comment: 15 pages, 1 TikZ figur

Construction of wedge-local nets of observables through Longo-Witten endomorphisms

A convenient framework to treat massless two-dimensional scattering theories has been established by Buchholz. In this framework, we show that the asymptotic algebra and the scattering matrix completely characterize the given theory under asymptotic completeness and standard assumptions. Then we obtain several families of interacting wedge-local nets by a purely von Neumann algebraic procedure. One particular case of them coincides with the deformation of chiral CFT by Buchholz-Lechner-Summers. In another case, we manage to determine completely the strictly local elements. Finally, using Longo-Witten endomorphisms on the U(1)-current net and the free fermion net, a large family of wedge-local nets is constructed.Comment: 33 pages, no figure. The final version is available under Open Access. CC-B

Conformal covariance and the split property

We show that for a conformal local net of observables on the circle, the split property is automatic. Both full conformal covariance (i.e. diffeomorphism covariance) and the circle-setting play essential roles in this fact, while by previously constructed examples it was already known that even on the circle, M\"obius covariance does not imply the split property. On the other hand, here we also provide an example of a local conformal net living on the two-dimensional Minkowski space, which - although being diffeomorphism covariant - does not have the split property.Comment: 34 pages, 3 tikz figure

Inclusions and positive cones of von Neumann algebras

We consider cones in a Hilbert space associated to two von Neumann algebras and determine when one algebra is included in the other. If a cone is assocated to a von Neumann algebra, the Jordan structure is naturally recovered from it and we can characterize projections of the given von Neumann algebra with the structure in some special situations.Comment: 20 pages, no figur

Solitons and nonsmooth diffeomorphisms in conformal nets

We show that any solitonic representation of a conformal (diffeomorphism covariant) net on S^1 has positive energy and construct an uncountable family of mutually inequivalent solitonic representations of any conformal net, using nonsmooth diffeomorphisms. On the loop group nets, we show that these representations induce representations of the subgroup of loops compactly supported in S^1 \ {-1} which do not extend to the whole loop group. In the case of the U(1)-current net, we extend the diffeomorphism covariance to the Sobolev diffeomorphisms D^s(S^1), s > 2, and show that the positive-energy vacuum representations of Diff_+(S^1) with integer central charges extend to D^s(S^1). The solitonic representations constructed above for the U(1)-current net and for Virasoro nets with integral central charge are continuously covariant with respect to the stabilizer subgroup of Diff_+(S^1) of -1 of the circle.Comment: 33 pages, 3 TikZ figure