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Poisson geometry of sigma models with extended supersymmetry. (English) Zbl 0999.81044
Summary: We consider a general \(N=(2,2)\) nonlinear sigma model with a torsion. We show that the consistency of \(N=(2,2)\) supersymmetry implies that the target manifold is necessary equipped with two (in general, different) Poisson structures. Finally we argue that the Poisson geometry of the target space is a characteristic feature of the sigma models with extended supersymmetry.

MSC:
81T10 Model quantum field theories
81T60 Supersymmetric field theories in quantum mechanics
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