Towards an operator-algebraic construction of integrable global gauge theories

TL;DR

This paper extends operator-algebraic methods to construct integrable quantum field theories with richer particle spectra and gauge symmetries, providing a framework for inverse scattering and asymptotic completeness.

Contribution

It introduces a new operator-algebraic construction for integrable models with multiple particle types and gauge groups, advancing the understanding of their local structure and scattering properties.

Findings

Constructed wedge-local quantum fields from two-particle S-matrices.

Argued the modular nuclearity condition likely holds in key models.

Demonstrated the construction solves the inverse scattering problem and proved asymptotic completeness.

Abstract

The recent construction of integrable quantum field theories on two-dimensional Minkowski space by operator-algebraic methods is extended to models with a richer particle spectrum, including finitely many massive particle species transforming under a global gauge group. Starting from a two-particle S-matrix satisfying the usual requirements (unitarity, Yang-Baxter equation, Poincar\'e and gauge invariance, crossing symmetry, ...), a pair of relatively wedge-local quantum fields is constructed which determines the field net of the model. Although the verification of the modular nuclearity condition as a criterion for the existence of local fields is not carried out in this paper, arguments are presented that suggest it holds in typical examples such as nonlinear O(N) sigma-models. It is also shown that for all models complying with this condition, the presented construction solves the inverse scattering problem by recovering the S-matrix from the model via Haag-Ruelle scattering theory, and a proof of asymptotic completeness is given.