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

TL;DR

This paper explores the complex structures, supersymmetry, and geometric properties of N=(2,2) WZW-models, illustrating their relation to generalized Kaehler and Calabi-Yau geometries through specific examples.

Contribution

It provides a detailed analysis of the geometric structures and supersymmetry conditions in N=(2,2) WZW-models, including type changing and superfield content, with explicit examples on S3xS1 and S3xS3.

Findings

Analysis of complex structures and type changing in WZW-models

Explicit examples on S3xS1 and S3xS3 confirming geometric properties

Identification of a weaker condition for N=(2,2) superconformal generalized Kaehler geometry

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.