D-branes on Group Manifolds and Deformation Quantization

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.Comment: 20 pages, harvmac file, no figures, corrected typo

Branes and Fluxes in Orientifolds and K-theory

RR fields in string backgrounds including orientifold planes and branes on top of them are classified by K-theory. Following the idea introduced in hep-th/0103183, we also classify such fluxes by cohomology. Both of them are compared through the Atiyah-Hirzebruch Spectral Sequence. Some new correlations between branes on orientifold planes $Op^\pm$ and obstructions to the existence of some branes are found. Finally, we find a topological condition that avoid the presence of global gauge anomalies in lower dimensional systems.Comment: 47 pages, latex, no figures. v4: Typos corrected, exposition improved. Main conclusions unchanged. To be published in Nuclear Physics