Some General Aspects of Coset Models and Topological Kazama-Suzuki Models

Abstract

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. We first generalize Witten's analysis of the holomorphic factorization of bosonic G/H models to models with N=1 and N=2 supersymmetry. 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, ...) of the topologically twisted G/H Kazama-Suzuki models. We explain how all of the above generalizes to non-trivial gauge bundles. 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.

expanded version to appear in NPB: construction of wave functions, proof of holomorphic factorization and localization extended to non-trivial gauge bundles; 73 pages, LaTeX file

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Cited by in corpus (6)

• Chern-Simons Theory on S^1-Bundles: Abelianisation and q-deformed Yang-Mills Theory
• Superconformal Coset Equivalence from Level-Rank Duality
• G/G models as the strong coupling limit of topologically massive gauge theory
• Grassmannian Topological Kazama-Suzuki Models and Cohomology
• Supergeometry in Equivariant Cohomology
• Berezin Quantization of Gauged WZW and Coset Models