Grassmannian topological Kazama-Suzuki models and cohomology

Oct, 1995
43 pages
Published in:
  • Nucl.Phys.B 488 (1997) 599-652
e-Print:
Report number:
  • IC-95-341,
  • ENSLAPP-L-557-95

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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 kk. We also analyze 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 (hep-th/9510187), we reduce the correlators to finite-dimensional purely algebraic expressions. As an application, these are evaluated explicitly for the CP(2)CP(2) model at level kk and shown for all kk to coincide with the cohomological intersection numbers of the two-plane Grassmannian G(2,k+2)G(2,k+2), thus realizing the level-rank duality between this model and the G(2,k+2)G(2,k+2) model at level one.
Note:
  • 44 pages (37 A4 pages); LaTeX file using amstex.sty (should work with 2e and 2.09; see instructions for use with A4 paper size and/or without amstex.sty) Report-no: IC/95/341, ENSLAPP-L-557/95
  • 11.25.Hf
  • 11.15.-q
  • 11.10 Kk
  • Coset models
  • Kazama-Suzuki
  • Localization
  • Chiral rings
  • Cohomology
  • Topological field theory
  • field theory: conformal