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

TL;DR

This paper introduces an operator-algebraic method to construct local, massive, and interacting quantum field models in two dimensions, providing new frameworks for understanding quantum field theories without relying on traditional nuclearity assumptions.

Contribution

The paper develops a novel operator-algebraic approach to build two-dimensional quantum field models using Longo-Witten endomorphisms, expanding the toolkit for constructing Haag-Kastler nets.

Findings

Constructed local, massive, interacting nets without modular nuclearity

Developed wedge-local nets via conformal net endomorphisms

Provided existence proofs for local observables in the models

Abstract

We present a procedure to construct families of local, massive and interacting Haag-Kastler nets on the two-dimensional spacetime through an operator-algebraic method. An existence proof of local observable is given without relying on modular nuclearity. By a similar technique, another family of wedge-local nets is constructed using certain endomorphisms of conformal nets recently studied by Longo and Witten.