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Into the amplituhedron

Arkani-Hamed, Nima and Trnka, Jaroslav (2014) Into the amplituhedron. Journal of High Energy Physics, 2014 (12). Art. No. 182. ISSN 1126-6708.

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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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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.
Funding AgencyGrant Number
Department of Energy (DOE)DE-FG02-91ER40654
David and Ellen Lee Postdoctoral ScholarshipUNSPECIFIED
Department of Energy (DOE)DE-FG03-92-ER40701
Subject Keywords:Supersymmetric gauge theory, Scattering Amplitudes
Issue or Number:12
Record Number:CaltechAUTHORS:20150202-084533756
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:54278
Deposited By: Tony Diaz
Deposited On:02 Feb 2015 19:21
Last Modified:03 Oct 2019 07:56

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