Abstract
We give a physical derivation of generalized Kähler geometry. Starting from a supersymmetric nonlinear sigma model, we rederive and explain the results of Gualtieri (Generalized complex geometry, DPhil thesis, Oxford University, 2004) regarding the equivalence between generalized Kähler geometry and the bi-hermitean geometry of Gates et al. (Nucl Phys B248:157, 1984). When cast in the language of supersymmetric sigma models, this relation maps precisely to that between the Lagrangian and the Hamiltonian formalisms. We also discuss topological twist in this context.
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Bredthauer, A., Lindström, U., Persson, J. et al. Generalized Kähler Geometry from Supersymmetric Sigma Models. Lett Math Phys 77, 291–308 (2006). https://doi.org/10.1007/s11005-006-0099-x
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DOI: https://doi.org/10.1007/s11005-006-0099-x