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 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 ≥ 2, we obtain examples of non Möbius-covariant sectors of a 3-regular (non 4-regular) net.

Let Jf a M be von-Neumann-Algebras on a Hubert space Jf, Ω a common cyclic and separating vector. Denote Δ M , Δjf resp. J My J^ the associated modular operators and conjugations. Assume Δ^ι t JfΔ^ι t a Jf for t ^ 0. We call such an inclusion half-sided modular. Then we prove the existence of a oneparameter unitary group U(a) on Jf, a e R, with generator --(In Δjr -In Δ M ) ^ 0 2π and relations 1. Δ%U(a)Δ^u = Δ^ΌiήΔy* = U(e~2 ilt a) for all a, ίe R, 2. J^ = 1/(2), 3. Δ%. = U(1)Δ%U( -1) for all te R 4. j" = υ{\)Jiυ{-i).If Ji is a factor and Ώ is also cyclic for Jf' n ,y# 5 we show that ^ has to be of type III,.

In this communication we present some new results on modular theory in the context of quantum field theory. In doing this we develop some new proposals how to generalize concepts of finite dimensional geometrical actions to infinite dimensional "hidden" symmetries. The latter are of a purely modular origin and remain hidden in any quantization approach. The spirit of this work is more on a programmatic side, with many details remaining to be elaborated.

In this letter we construct a representation of the 3+1-dimensional Poincaré group by modular groups of von Neumann algebras lying in a specified modular position with respect to each other. Combining this new result with an old one of Bisognano–Wichmann [J. Math. Phys. 16, 985 (1975)] we obtain a net of local observables of a 3+1-dimensional quantum field theory out of a finite set of algebras.

In thermal states of chiral theories, as recently investigated by H.-J. Borchers and J. Yngvason, there exists a rich group of hidden symmetries. Here we show that this leads to a radical converse of of the Hawking-Unruh observation in the following sense. The algebraic commutant of the algebra associated with a (heat bath) thermal chiral system can be used to reprocess the thermal system into a ground state system on a larger algebra with a larger localization space-time. This happens in such a way that the original system appears as a kind of generalized Unruh restriction of the ground state sytem and the thermal commutant as being transmutated into newly created "virgin space-time region" behind a horizon. The related concepts of a "chiral conformal core" and the possibility of a "blow-up" of the latter suggest interesting ideas on localization of degrees of freedom with possible repercussion on how to define quantum entropy of localized matter content in Local Quantum Physics.