On All-loop Integrands of Scattering Amplitudes in Planar N=4 SYM

Details On All-loop Integrands of Scattering Amplitudes in Planar N=4 SYM On All-loop Integrands of Scattering Amplitudes in Planar N=4 SYM

2010-10-29

arxiv.org/abs/1010.6256v2

JHEP 1102:116,2011

Physics

High Energy Physics

High Energy Physics - Theory

34 pages, 17 figures; v2: Minor improvements to exposition and discussion, updated references, typos fixed

Scientific paper

10.1007/JHEP02(2011)116

We study the relationship between the momentum twistor MHV vertex expansion of planar amplitudes in N=4 super-Yang-Mills and the all-loop generalization of the BCFW recursion relations. We demonstrate explicitly in several examples that the MHV vertex expressions for tree-level amplitudes and loop integrands satisfy the recursion relations. Furthermore, we introduce a rewriting of the MHV expansion in terms of sums over non-crossing partitions and show that this cyclically invariant formula satisfies the recursion relations for all numbers of legs and all loop orders.

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