D-branes on Group Manifolds and Deformation Quantization

Details D-branes on Group Manifolds and Deformation Quantization D-branes on Group Manifolds and Deformation Quantization

1999-07-24

arxiv.org/abs/hep-th/9907183v2

Nucl.Phys. B618 (2001) 81-98

Physics

High Energy Physics

High Energy Physics - Theory

20 pages, harvmac file, no figures, corrected typos

Scientific paper

10.1016/S0550-3213(01)00503-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.

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