  In this note we explain how world-volume geometries of D-branes can be
reconstructed within the microscopic framework where D-branes are described
through boundary conformal field theory. We extract the (non-commutative)
world-volume algebras from the operator product expansions of open string
vertex operators. For branes in a flat background with constant non-vanishing
B-field, the operator products are computed perturbatively to all orders in the
field strength. The resulting series coincides with Kontsevich's presentation
of the Moyal product. After extending these considerations to fermionic fields
we conclude with some remarks on the generalization of our approach to curved
backgrounds.
