Supersymmetric WZ-Poisson sigma model and twisted generalized complex geometry

Details Supersymmetric WZ-Poisson sigma model and twisted generalized complex geometry Supersymmetric WZ-Poisson sigma model and twisted generalized complex geometry

2005-11-17

arxiv.org/abs/hep-th/0511179v3

Lett.Math.Phys.77:53-62,2006

Physics

High Energy Physics

High Energy Physics - Theory

11 pages. Proof of the theorem of Section 2 revised. Typos corrected. Version to appear in Lett.Math.Phys

Scientific paper

10.1007/s11005-006-0080-8

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.

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