  We prove a version of Kontsevich's formality theorem for two subspaces
(branes) of a vector space $X$. The result implies in particular that the
Kontsevich deformation quantizations of $\mathrm{S}(X^*)$ and $\wedge(X)$
associated with a quadratic Poisson structure are Koszul dual. This answers an
open question in Shoikhet's recent paper on Koszul duality in deformation
quantization.
