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

TL;DR

This paper develops a von Neumann algebraic framework for constructing and analyzing wedge-local nets of observables in two-dimensional massless quantum field theories, utilizing Longo-Witten endomorphisms to generate new models.

Contribution

It introduces a novel algebraic method to construct wedge-local nets, including deformations of chiral CFTs and nets with explicitly determined local elements, using Longo-Witten endomorphisms.

Findings

Characterization of theories via asymptotic algebra and scattering matrix

Construction of new wedge-local nets through algebraic deformations

Explicit determination of strictly local elements in some models

Abstract

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.