  Perturbative scattering amplitudes in Yang-Mills theory have many unexpected
properties, such as holomorphy of the maximally helicity violating amplitudes.
To interpret these results, we Fourier transform the scattering amplitudes from
momentum space to twistor space, and argue that the transformed amplitudes are
supported on certain holomorphic curves. This in turn is apparently a
consequence of an equivalence between the perturbative expansion of ${\cal
N}=4$ super Yang-Mills theory and the $D$-instanton expansion of a certain
string theory, namely the topological $B$ model whose target space is the
Calabi-Yau supermanifold $\Bbb{CP}^{3|4}$.
