logo Branes in Poisson sigma models and deformation quantization

After a short review of the description of deformation quantization of Poisson manifolds in terms of topological sigma models with free boundary conditions, we turn to more recent results and work in progress with A. Cattaneo on Dirichlet boundary conditions (D-branes).
In the case of one D-brane this gives associative deformations of the algebra of functions on manifolds obtained by Hamiltonian reduction.
The associated relative formality theorem is reduced by a duality transformation to a formality theorem for supermanifolds.
Intersecting D-branes are related to bimodules over the deformed algebras of functions.