D-branes on Group Manifolds and Deformation Quantization
arXiv:hep-th/9907183 · doi:10.1016/S0550-3213(01)00503-X
Abstract
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.
20 pages, harvmac file, no figures, corrected typos
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Cited by in corpus (6)
- Quantum Field Theory on Noncommutative Spaces
- Non-commutative World-volume Geometries: Branes on SU(2) and Fuzzy Spheres
- Noncommutative D-Brane in Non-Constant NS-NS B Field Background
- Chiral Bosons in Noncommutative Spacetime
- BRST construction of D-branes in SU(2) WZW model
- On the geometry of coset branes