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Into the Amplituhedron · Around

2013

Into the Amplituhedron

Arkani-Hamed, Nima, Trnka, Jaroslav

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We initiate an exploration of the physics and geometry of the amplituhedron, starting with the simplest case of the integrand for four-particle scattering in planar N=4 SYM.

We show how the textbook structure of the unitarity double-cut follows from the positive geometry.
We also use the geometry to expose the behavior of the multicollinear limit, providing a direct motivation for studying the logarithm of the amplitude.
In addition to computing the two and three-loop integrands, we explore various lower-dimensional faces of the amplituhedron, thereby computing non-trivial cuts of the integrand to all loop orders.

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N. Beisert and M. Staudacher, Nucl. Phys. B 670
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R. Britto, F. Cachazo, B. Feng and E. Witten, Phys. Rev. Lett. 94
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B. Eden and M. Staudacher, J. Stat. Mech. 0611
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N. Arkani-Hamed and J. Trnka, arXiv:1312.2007 [hep-th]
Original
2007
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Z. Bern, M. Czakon, L. J. Dixon, D. A. Kosower and V. A. Smirnov, Phys. Rev. D 75
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