English

D-branes on Group Manifolds and Deformation Quantization

High Energy Physics - Theory 2009-10-31 v2 Quantum Algebra

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.

Keywords

Cite

@article{arxiv.hep-th/9907183,
  title  = {D-branes on Group Manifolds and Deformation Quantization},
  author = {Hugo Garcia-Compean and Jerzy F. Plebanski},
  journal= {arXiv preprint arXiv:hep-th/9907183},
  year   = {2009}
}

Comments

20 pages, harvmac file, no figures, corrected typos

R2 v1 2026-07-22T16:16:37.135Z