Line bundles in supersymmetric coset models

The scalars of a N = 1 supersymmetric σ-model in 4 dimensions parametrize a Kähler manifold. This Kähler manifold often takes the form of a tensor product of bundles over a basis manifold. When one of these bundles is a line bundle, the corresponding Kähler form has to satisfy a quantization condition when the topology of the submanifold is non-trivial. This results in a consistency restriction on the construction of anomaly free models. We determine the smallest Kähler potentials that satisfy this cocycle condition for any Kählerian coset space G/H, where H is the centralizer of a torus of a compact Lie group G. In this way we obtain a constructive proof of a theorem by Borel-Weyl that classifies the elements of the (co)homology groups of G/H. Using these results we discuss the consistency of anomaly free models based on the coset spaces E6/SO(10) × U(1) and SU(5)/SU(2) × U(1)× SU(3). PACS: 02.20.Sv, 02.40.-k, 12.60.Jv, 11.30.Na.