The generalized Kaehler geometry of N=(2,2) WZW-models

Abstract

N=(2,2), d=2 supersymmetric non-linear sigma-models provide a physical realization of Hitchin's and Gualtieri's generalized Kaehler geometry. A large subclass of such models are comprised by WZW-models on even-dimensional reductive group manifolds. In the present paper we analyze the complex structures, type changing, the superfield content and the affine isometries compatible with the extra supersymmetry. The results are illustrated by an exhaustive discussion of the N=(2,2) WZW-models on S3xS1 and S3xS3 where various aspects of generalized Kaehler and Calabi-Yau geometry are verified and clarified. The examples illustrate a slightly weaker definition for an N=(2,2) superconformal generalized Kaehler geometry compared to that for a generalized Calabi-Yau geometry.

LaTeX, 51 pages, Typo's corrected, discussion on superconformal vs. generalized Calabi-Yau fine tuned

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• The Semi-Chiral Quotient, Hyperkahler Manifolds and T-duality
• Extended supersymmetry of semichiral sigma model in 4D
• Generalized Kahler structures on group manifolds and T-duality
• Semichirals and Four Dimensional Geometry
• Generalized K$\ddot{a}$hler Geometry in Kazama-Suzuki coset models
• Doubled space and extended supersymmetry