The Grassmannian and the twistor string: Connecting all trees in N = 4 SYM

We present a new, explicit formula for all tree-level amplitudes in N = 4 super Yang-Mills. The formula is written as a certain contour integral of the connected prescription of Witten's twistor string, expressed in link variables. A very simple deformation of the integrand gives directly the Grassmannian integrand proposed in [1] together with the explicit contour of integration. The integral is derived by iteratively adding particles to the Grassmannian integral, one particle at a time, and makes manifest both parity and soft limits. The formula is shown to be related to that of [2], and generalizes the results of [3, 4] for NMHV and N²MHV to all N(^k-2)MHV tree amplitudes in N = 4 super Yang-Mills.