Some general aspects of coset models and topological Kazama-Suzuki models

We study global aspects of N = 2 Kazama-Suzuki coset models by investigating topological G/ H Kazama-Suzuki models in a Lagrangian framework based on gauged Wess-Zumino-Witten models. To that end, we first generalize Witten's analysis of the holomorphic factorization of bosonic G/ H models to models with N = 1 and N = 2 supersymmetry, in the course of which we also find some new anomaly-free and supersymmetric models based on non-diagonal embeddings of the gauge group. We then explain the basic properties (action, symmetries, metric independence, etc.) of the topologically twisted G/ H Kazama-Suzuki models. As non-trivial gauge bundles unavoidably occur, we explain how all of the above generalizes to that case. We employ the path integral methods of localization and abelianization (shown to be valid also for non-trivial bundles) to establish that the twisted G/ H models can be localized to bosonic H/ H models (with certain quantum corrections), and can hence be reduced to an abelian bosonic T/ T model, T a maximal torus of H. We also present the action and the symmetries of the coupling of these models to topological gravity. We determine the bosonic observables for all the models based on classical flag manifolds and the bosonic observables and their fermionic descendants for models based on complex Grassmannians. These results will be used in subsequent publications to calculate explicitly the chiral primary ring of Kazama-Suzuki models.