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The S-matrix for planar N = 4 super Yang-Mills theory can be computed as thecorrelation function for a holomorphic polygonal Wilson loop in twistor space.In an axial gauge, this leads to the construction of the all-loop integrand viaMHV diagrams in twistor space. We show that at MHV, this formulation leadsdirectly to expressions for loop integrands in d log form; i.e., the integrandis a product of exterior derivatives of logarithms of rational functions. Forhigher MHV degree, it is in d log form multiplied by delta functions. Theparameters appearing in the d log form arise geometrically as the coordinatesof insertion points of propagators on the holomorphic Wilson loop or on MHVvertices. We discuss a number of examples at one and two loops and give apreliminary discussion of the evaluation of the 1-loop MHV amplitude.

From the Holomorphic Wilson Loop to `d log' Loop-Integrands of Super-Yang-Mills Amplitudes