%0 Journal Article
%T D-branes on Group Manifolds and Deformation Quantization
%A Hugo Garcia-Compean
%A Jerzy F. Plebanski
%J Mathematics
%D 1999
%I arXiv
%R 10.1016/S0550-3213(01)00503-X
%X Recently M. Kontsevich found a combinatorial formula defining a star-product of deformation quantization for any Poisson manifold. Kontsevich's 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 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 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.
%U http://arxiv.org/abs/hep-th/9907183v2