  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.
