Supersymmetric WZ-Poisson sigma model and twisted generalized complex geometry

TL;DR

This paper explores the supersymmetric WZ-Poisson sigma model within twisted generalized complex geometry, simplifying compatibility conditions and revealing their geometric interpretation using contravariant connections.

Contribution

It demonstrates that in the Hamiltonian formalism, the compatibility conditions reduce to an algebraic equation with a natural geometric interpretation, simplifying the analysis of the model.

Findings

Compatibility conditions reduce to an algebraic equation

Algebraic condition has a natural geometric interpretation

Contravariant connections are useful in the analysis

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.