Recursion Relations, Generating Functions, and Unitarity Sums in N=4 SYM Theory

Abstract

We prove that the MHV vertex expansion is valid for any NMHV tree amplitude of N=4 SYM. The proof uses induction to show that there always exists a complex deformation of three external momenta such that the amplitude falls off at least as fast as 1/z for large z. This validates the generating function for n-point NMHV tree amplitudes. We also develop generating functions for anti-MHV and anti-NMHV amplitudes. As an application, we use these generating functions to evaluate several examples of intermediate state sums on unitarity cuts of 1-, 2-, 3- and 4-loop amplitudes. In a separate analysis, we extend the recent results of arXiv:0808.0504 to prove that there exists a valid 2-line shift for any n-point tree amplitude of N=4 SYM. This implies that there is a BCFW recursion relation for any tree amplitude of the theory.

42pp, 7 figures; v2: completion of 4-loop spin sum, typos corrected, new figure added

References in corpus (2)

• A note on dual superconformal symmetry of the N=4 super Yang-Mills S-matrix
• Generating Tree Amplitudes in N=4 SYM and N=8 SG

Cited by in corpus (7)

• Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory
• Scattering in Mass-Deformed N>=4 Chern-Simons Models
• Proof of the MHV vertex expansion for all tree amplitudes in N=4 SYM theory
• One-Loop Amplitudes in N=4 Super Yang-Mills and Anomalous Dual Conformal Symmetry
• A super MHV vertex expansion for N=4 SYM theory
• One-loop N=8 supergravity coefficients from N=4 super Yang-Mills
• Supersymmetric Yang-Mills and Supergravity Amplitudes at One Loop