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

Understand

It is well-known that sigma-models with symmetric target spaces are classically integrable.

• At 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-parametric family of connections, which can be a sign of integrability of the theory.
• We also elaborate on geometric aspects of the proposed model.