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

TL;DR

This paper explores the global properties of N=2 Kazama-Suzuki coset models, extending holomorphic factorization analysis, identifying new anomaly-free models, and applying localization techniques to simplify their structure.

Contribution

It generalizes Witten's analysis to N=2 models, finds new anomaly-free embeddings, and demonstrates localization to simpler bosonic models within topological Kazama-Suzuki frameworks.

Findings

Extended holomorphic factorization to N=2 models

Identified new anomaly-free gauge embeddings

Localized models to bosonic H/H and T/T 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.