Proof of the MHV vertex expansion for all tree amplitudes in N=4 SYM theory

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We prove the MHV vertex expansion for all tree amplitudes of N=4 SYM theory.

• The proof uses a shift acting on all external momenta, and we show that every N^kMHV tree amplitude falls off as 1/z^k, or faster, for large z under this shift.
• The MHV vertex expansion allows us to derive compact and efficient generating functions for all N^kMHV tree amplitudes of the theory.
• We also derive an improved form of the anti-NMHV generating function.