# Towards an operator-algebraic construction of integrable global gauge theories

August 11, 2012

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, Poincaré 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.

Keywords:

constructive AQFT, integrable models, two-dimensional models, global gauge theories, inverse scattering