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Published December 31, 2014 | Submitted + Published
Journal Article Open

Into the amplituhedron


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.

Additional Information

© 2014 The Authors. Published for SISSA by Springer. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. Article funded by SCOAP3. Received: September 4, 2014; Accepted: December 9, 2014; Published: December 31, 2014. We thank Jake Bourjaily, Freddy Cachazo, Simon Caron-Huot, Johannes Henn, Andrew Hodges, Jan Plefka, Dave Skinner and Matthias Staudacher for stimulating discussions. N. A.-H. is supported by the Department of Energy under grant number DE-FG02-91ER40654. J. T. is supported in part by the David and Ellen Lee Postdoctoral Scholarship and by DOE grant DE-FG03-92-ER40701 and also by NSF grant PHY-0756966.

Attached Files

Published - art_10.1007_JHEP12_2014_182.pdf

Submitted - 1312.7878v1.pdf


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