Grassmannian Topological Kazama-Suzuki Models and Cohomology

TL;DR

This paper explores the topological sectors of Grassmannian-based Kazama-Suzuki models, revealing their observable rings match classical cohomology and uncovering level-rank dualities through algebraic and geometric analysis.

Contribution

It demonstrates the correspondence between the observable ring in topological sectors and Grassmannian cohomology, and uncovers a hierarchy of level-rank relations among models.

Findings

Observable ring matches Grassmannian cohomology

Explicit evaluation of correlators for CP2 model

Identification of level-rank duality in models

Abstract

We investigate in detail the topological gauged Wess-Zumino-Witten models describing topological Kazama-Suzuki models based on complex Grassmannians. We show that there is a topological sector in which the ring of observables (constructed from the Grassmann odd scalars of the theory) coincides with the classical cohomology ring of the Grassmannian for all values of the level k. We perform a detailed analysis of the non-trivial topological sectors arising from the adjoint gauging, and investigate the general ring structure of bosonic correlation functions, uncovering a whole hierarchy of level-rank relations (including the standard level-rank duality) among models based on different Grassmannians. Using the previously established localization of the topological Kazama-Suzuki model to an Abelian topological field theory, we reduce the correlators to finite-dimensional purely algebraic expressions. As an application, these are evaluated explicitly for the CP{2} model at level k and shown for all k to coincide with the cohomological intersection numbers of the two-plane Grassmannian G(2,k+2), thus realizing the level-rank duality between this model and the G(2,k+2) model at level one.