D-branes on group manifolds and deformation quantization Original Research Article

Recently M. Kontsevich found a combinatorial formula defining a star-product of deformation quantization for any Poisson manifold. Kontsevichʹs formula has been reinterpreted physically as quantum correlation functions of a topological sigma model for open strings as well as in the context of D-branes in flat backgrounds with a Neveu–Schwarz B-field. Here the corresponding Kontsevichʹs formula for the dual of a Lie algebra is derived in terms of the formalism of D-branes on group manifolds. In particular we show that that formula is encoded at the two-point correlation functions of the Wess–Zumino–Witten effective theory with Dirichlet boundary conditions. The B-field entering in the formalism plays an important role in this derivation.