Flag manifold σ-models: The $\frac{1}{N}$-expansion and the anomaly two-form

We construct a gauged linear sigma-model representation and develop a $\frac{1}{N}$-expansion for flag manifold σ-models previously proposed by the author. Classically there exists a zero-curvature representation for the equations of motion of these models, which leads in particular to the existence of a conserved non-local charge. We show that at the quantum level this charge is no longer conserved and calculate explicitly the anomaly in its conservation law.