  We argue that there exists a derived equivalence between Calabi-Yau
threefolds obtained by taking dual hyperplane sections (of the appropriate
codimension) of the Grassmannian G(2, 7) and the Pfaffian Pf(7). The existence
of such an equivalence has been conjectured by physicists for almost ten years,
as the two families of Calabi-Yau threefolds are believed to have the same
mirror. It is the first example of a derived equivalence between Calabi-Yau
threefolds which are provably non-birational.
