  We derive an expression for parton scattering amplitudes of planar gauge
theory in terms of sums of Wilson loops. We study in detail the example of
Yang-Mills theory with an adjoint Higgs field. The expression exhibits the
T-duality performed by Alday and Maldacena in the AdS dual as a Fourier
transform in loop space. When combined with the AdS/CFT correspondence for
Wilson loops and a strong coupling argument for the dominance of 1PI diagrams,
this leads to a derivation of the Alday-Maldacena holographic prescription for
scattering amplitudes in terms of momentum Wilson loops. The formula leads to a
conjecture for a relationship between position-space and momentum-space Wilson
loops in N=4 SYM at finite coupling.
