Recursion relations, generating functions, and unitarity sums in N=4 SYM theory
Author(s)Elvang, Henriette; Freedman, Daniel Z.; Kiermaier, Michael
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We prove that the MHV vertex expansion is valid for any NMHV tree amplitude of Script 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 Script N = 4 SYM. This implies that there is a BCFW recursion relation for any tree amplitude of the theory.
DepartmentMassachusetts Institute of Technology. Center for Theoretical Physics; Massachusetts Institute of Technology. Department of Mathematics
Journal of High Energy Physics
Institute of Physics
Henriette Elvang, Daniel Z. Freedmana, and Michael Kiermaier. "Recursion relations, generating functions, and unitarity sums in N = 4 SYM theory." Journal of High Energy Physics, April 2009.
Author's final manuscript