Integrable properties of σ-models with non-symmetric target spaces

It is well known that σ  -models with symmetric target spaces are classically integrable. With the example of the model with target space the flag manifold U(3)U(1)3 – a non-symmetric space – we show that the introduction of torsion allows to cast the equations of motion in the form of a zero-curvature condition for a one-parameter family of connections, which can be a sign of integrability of the theory. We also elaborate on geometric aspects of the proposed model.