Poisson Sigma Models and String Theory

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Open string theories in generic background fields induce a noncommutative structure on D-branes present in the low energy effective field theories. This is proven only for particular, rather simple backgrounds, but believed to hold much more generally. The expected noncommutative geometries, on the other hand, are provided by the Kontsevich formula which is again described by a very special class of (topological) string theories, namely the so-called Poisson Sigma Models. It is intended to establish the precise relation between brane non-commutative geometry and some limiting Poisson Sigma Model for arbitrary curved string backgrounds. Furthermore, we want to use this relation for constructing the non-commutative gauge theories that describe the dynamics of branes in general curved backgrounds. In this context, it will be also interesting to propose and study new topological generalizations of the Poisson sigma model that are both motivated by more general string backgrounds (e.g. with NS or RR-fluxes) and by their relation with various generalizations of Poisson geometry that have been considered in Mathematics recently (such as e.g. Dirac-structures).