A path integral approach to the Kontsevich quantization formula

We give a quantum field theory interpretation of Kontsevich's deformation q uantization 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 superconf ormal field theory. The associativity of the star product, and more general ly 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.