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Generalized Kähler manifolds and off-shell supersymmetry. (English) Zbl 1114.81077
Summary: We solve the long standing problem of finding an off-shell supersymmetric formulation for a general $$N = (2, 2)$$ nonlinear two dimensional sigma model. Geometrically the problem is equivalent to proving the existence of special coordinates; these correspond to particular superfields that allow for a superspace description. We construct and explain the geometric significance of the generalized Kähler potential for any generalized Kähler manifold; this potential is the superspace Lagrangian.

##### MSC:
 81T60 Supersymmetric field theories in quantum mechanics 53C55 Global differential geometry of Hermitian and Kählerian manifolds 32Q15 Kähler manifolds 81T10 Model quantum field theories 81R12 Groups and algebras in quantum theory and relations with integrable systems
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