Some general aspects of coset models and topological KazamaSuzuki models
Abstract
We study global aspects of N = 2 KazamaSuzuki coset models by investigating topological G/ H KazamaSuzuki models in a Lagrangian framework based on gauged WessZuminoWitten 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 anomalyfree and supersymmetric models based on nondiagonal embeddings of the gauge group. We then explain the basic properties (action, symmetries, metric independence, etc.) of the topologically twisted G/ H KazamaSuzuki models. As nontrivial 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 nontrivial 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 KazamaSuzuki models.
 Publication:

Nuclear Physics B
 Pub Date:
 February 1997
 DOI:
 10.1016/S05503213(97)000072
 arXiv:
 arXiv:hepth/9510187
 Bibcode:
 1997NuPhB.488..541B
 Keywords:

 High Energy Physics  Theory
 EPrint:
 expanded version to appear in NPB: construction of wave functions, proof of holomorphic factorization and localization extended to nontrivial gauge bundles