D-branes on group manifolds and deformation quantization

Recently M. Kontsevich found a combinatorial formula defining a star-produc t of deformation quantization for any Poisson manifold. Kontsevich's formul a has been reinterpreted physically as quantum correlation functions of a t opological sigma model for open strings as well as in the context of D-bran es in flat backgrounds with a Neveu-Schwarz B-field. Here the corresponding Kontsevich's 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 th at formula is encoded at the two-point correlation functions of the Wess-Zu mino-Witten effective theory with Dirichlet boundary conditions. The B-fiel d entering in the formalism plays an important role in this derivation. (C) 2001 Elsevier Science B.V. All rights reserved.