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2010

The All-Loop Integrand For Scattering Amplitudes in Planar N=4 SYM

Arkani-Hamed, Nima, Bourjaily, Jacob L., Cachazo, Freddy et al.

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We give an explicit recursive formula for the all L-loop integrand for scattering amplitudes in N=4 SYM in the planar limit, manifesting the full Yangian symmetry of the theory.

This generalizes the BCFW recursion relation for tree amplitudes to all loop orders, and extends the Grassmannian duality for leading singularities to the full amplitude.
It also provides a new physical picture for the meaning of loops, associated with canonical operations for removing particles in a Yangian-invariant way.
Loop amplitudes arise from the "entangled" removal of pairs of particles, and are naturally presented as an integral over lines in momentum-twistor space.

The All-Loop Integrand For Scattering Amplitudes in Planar N=4 SYM · Around

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Wiley, New York, 1978
P. Griffiths and J. Harris, Principles of Algebraic Geometry · 1978
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