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Supersymmetric WZ-Poisson Sigma Model and Twisted Generalized Complex Geometry

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Abstract

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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  1. Departamento de Física Teórica, Universidad de Zaragoza, Pedro Cerbuna 12, 50009, Zaragoza, Spain

    Iván Calvo

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  1. Iván Calvo
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Calvo, I. Supersymmetric WZ-Poisson Sigma Model and Twisted Generalized Complex Geometry. Lett Math Phys 77, 53–62 (2006). https://doi.org/10.1007/s11005-006-0080-8

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  • DOI: https://doi.org/10.1007/s11005-006-0080-8

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