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N=(2,2), d=2 supersymmetric non-linear sigma-models provide a physical realization of Hitchin's and Gualtieri's generalized Kaehler geometry.
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U. Lindström, M. Roček, I. Ryb, R. von Unge and M. Zabzine, T-duality and Generalized Kahler Geometry, J. High Energy Phys
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2003
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M. Gualtieri, Generalized complex geometry, Oxford University DPhil thesis, 2003,
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U. Lindström, M. Roček, R. von Unge and M. Zabzine, Generalized Kähler manifolds and off-shell supersymmetry, Commun. Math. Phys
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Martin Roček: private communication and work in progress
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N. Halmagyi, A. Tomasiello, Generalized Kaehler Potentials from Supergravity,’ Commun. Math. Phys
2009
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