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

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dc.creatorElvang, Henriette
dc.creatorFreedman, Daniel Z.
dc.creatorKiermaier, Michael
dc.date2008-08-12
dc.date2008-12-20
dc.date.accessioned2026-07-07T13:04:38Z
dc.date.available2026-07-07T13:04:38Z
dc.descriptionWe 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.
dc.description42pp, 7 figures; v2: completion of 4-loop spin sum, typos corrected, new figure added
dc.identifierhttps://arxiv.org/abs/0808.1720
dc.identifierhttp://arxiv.org/abs/0808.1720
dc.identifierJHEP 0904:009,2009
dc.identifierdoi:10.1088/1126-6708/2009/04/009
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/227231
dc.subjectHigh Energy Physics - Theory
dc.titleRecursion Relations, Generating Functions, and Unitarity Sums in N=4 SYM Theory
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