A duality for the S matrix

@article{ArkaniHamed2009ADF,
  title={A duality for the S matrix},
  author={Nima Arkani-Hamed and Freddy Cachazo and Clifford Cheung and Jared Kaplan},
  journal={Journal of High Energy Physics},
  year={2009},
  volume={2010},
  pages={1-70}
}
We propose a dual formulation for the S Matrix of $$ \mathcal N $$ = 4 SYM. The dual provides a basis for the “leading singularities” of scattering amplitudes to all orders in perturbation theory, which are sharply defined, IR safe data that uniquely determine the full amplitudes at tree level and 1-loop, and are conjectured to do so at all loop orders. The scattering amplitude for n particles in the sector with k negative helicity gluons is associated with a simple integral over the space of k… 

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