1999/02/28 by Alberto S. Cattaneo, Giovanni Felder · 14 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Homotopy and Cohomology in Algebraic Topology #hep-th #math-ph #math.MP #math.QA
paper · pdf · doi:10.1007/s002200000229
published as Commun.Math.Phys. 212 (2000) 591-611 · 22 pages, 2 figures, references added. Conjecture on the center made more precise
arxiv created 1999/04/19 · openalex publication_date 2000/08/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We give a quantum field theory interpretation of Kontsevich's deformation quantization formula for Poisson manifolds. We show that it is given by the perturbative expansion of the path integral of a simple topological bosonic open string theory. Its Batalin-Vilkovisky quantization yields a superconformal field theory. The associativity of the star product, and more generally the formality conjecture can then be understood by field theory methods. As an application, we compute the center of the deformed algebra in terms of the center of the Poisson algebra.