Construction of two-dimensional quantum field models through Longo-Witten endomorphisms (Q2879420)

In the Haag-Kastler approach to quantum field theory, particular models are given as nets of von Neumann algebras. The main objective in this article is the construction of two-dimensional nets with nontrivial S-matrix. Borchers proved that it suffices to have a triple consisting of a von Neumann algebra associated with a wedge-shaped region, a unitary representation of spacetime translations, and the vacuum vector. And so the general strategy for the construction of the full Haag-Kastler net always was: first to construct the Borchers triple and to prove the cyclicity of the vacuum. This road has been followed by Lechner in a number of papers, while relying on modular nuclearity. In another series of papers written by Tanimoto, the main ingredients come from chiral conformal field theory. In the present paper, a family of wedge-local nets is constructed using endomorhisms recently introduced by Longo and Witten. The main result seems the proof of strict locality of the field theoretical models, i.e. the existence of observables in compactly localized regions.