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

Abstract

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. The proof leads to a curious set of sum rules for the diagrams of the MHV vertex expansion.

40 pages, 7 figures

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Cited by in corpus (11)

• On-shell constructibility of tree amplitudes in general field theories
• MHV Diagrams in Momentum Twistor Space
• The Six-Point NMHV amplitude in Maximally Supersymmetric Yang-Mills Theory
• One-Loop Amplitudes in N=4 Super Yang-Mills and Anomalous Dual Conformal Symmetry
• Symmetries of the N=4 SYM S-matrix
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• A super MHV vertex expansion for N=4 SYM theory
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