GRASSMANNIAN TOPOLOGICAL KAZAMA-SUZUKI MODELS AND COHOMOLOGY

We investigate in detail the topological gauged Wess-Zumino-Witten mod els describing topological Kazama-Suzuki models based on complex Grass mannians. We show that there is a topological sector in which the ring of observables (constructed from the Grassmann-odd scalars of the the ory) coincides with the classical cohomology ring of the Grassmannian for all values of the level k, We perform a detailed analysis of the n on-trivial topological sectors arising from the adjoint gauging, and i nvestigate 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 Grassmann ians, 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. A s an application, these are evaluated explicitly for the CP(2) model a t level k and shown for all k to coincide with the cohomological inter section numbers of the two-plane Grassmannian G(2, k + 2), thus realiz ing the level-rank duality between this model and the G(2, k + 2) mode l at level one. (C) 1997 Elsevier Science B.V.