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Supersymmetric WZ-Poisson sigma model and twisted generalized complex geometry. (English) Zbl 1105.53063
Summary: It has been shown recently that extended supersymmetry in twisted first-order sigma models is related to twisted generalized complex geometry in the target. In the general case there are additional algebraic and differential conditions relating the twisted generalized complex structure and the geometrical data defining the model. We study in the Hamiltonian formalism the case of vanishing metric, which is the supersymmetric version of the WZ-Poisson sigma model. We prove that the compatibility conditions reduce to an algebraic equation, which represents a considerable simplification with respect to the general case. We also show that this algebraic condition has a very natural geometrical interpretation. In the derivation of these results the notion of contravariant connections on twisted Poisson manifolds turns out to be very useful.

MSC:
53D17 Poisson manifolds; Poisson groupoids and algebroids
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
53C80 Applications of global differential geometry to the sciences
81T60 Supersymmetric field theories in quantum mechanics
81T10 Model quantum field theories
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