  We show that flag manifold $\sigma$-models (including $\mathbb{CP}^{n-1}$,
Grassmannian models as special cases) and their deformed versions may be cast
in the form of gauged bosonic Thirring/Gross-Neveu-type systems. Quantum
mechanically the gauging is violated by chiral anomalies, which may be
cancelled by adding fermions. We conjecture that such models are integrable and
check on some examples that the trigonometrically deformed geometries satisfy
the generalized Ricci flow equations.
