221 research outputs found
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
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
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
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
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