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Generalized Kähler geometry from supersymmetric sigma models. (English) Zbl 1105.53053
Summary: We give a physical derivation of generalized Kähler geometry. Starting from a supersymmetric nonlinear sigma model, we rederive and explain the results of M. Gualtieri [“Generalized complex geometry”, DPhil thesis, Oxford University, (2004)] regarding the equivalence between generalized Kähler geometry and the bi-hermitean geometry of S. J. Gates, C. M. Hull and M. Roček [Nucl. Phys. B 248, 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.

53C55 Global differential geometry of Hermitian and Kählerian manifolds
53B35 Local differential geometry of Hermitian and Kählerian structures
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
81T60 Supersymmetric field theories in quantum mechanics
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