Renormalization properties of bosonic non-linear σ-models built on compact homogeneous Kaehler manifolds

The non-linear bosonic σ-models built on compact Kaehler homogeneous manifolds are parametrized in such a way that multiplicative renormalizability holds, to all orders of perturbation theory. Moreover, the fields are not renormalized. The essential ingredients of the proof are the homogeneity of the space and the existence of a charge Y that separates the fields in φ and anti φ. (orig.)