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Published October 6, 2014 | Submitted + Published
Journal Article Open

The Amplituhedron


Perturbative scattering amplitudes in gauge theories have remarkable simplicity and hidden infinite dimensional symmetries that are completely obscured in the conventional formulation of field theory using Feynman diagrams. This suggests the existence of a new understanding for scattering amplitudes where locality and unitarity do not play a central role but are derived consequences from a different starting point. In this note we provide such an understanding for N=4 SYM scattering amplitudes in the planar limit, which we identify as "the volume" of a new mathematical object — the Amplituhedron — generalizing the positive Grassmannian. Locality and unitarity emerge hand-in-hand from positive geometry.

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© 2013 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: September 8, 2014; Published: October 6, 2014. We thank Zvi Bern, Jake Bourjaily, Freddy Cachazo, Simon Caron-Huot, Clifford Cheung, Pierre Deligne, Lance Dixon, James Drummond, Sasha Goncharov, Song He, Johannes Henn, Andrew Hodges, Yu-tin Huang, Jared Kaplan, Gregory Korchemsky, David Kosower, Bob MacPherson, Juan Maldacena, Lionel Mason, David McGady, Jan Plefka, Alex Postnikov, Amit Sever, Dave Skinner, Mark Spradlin, Matthias Staudacher, Hugh Thomas, Pedro Vieira, Anastasia Volovich, Lauren Williams and Edward Witten for valuable discussions. Our research in this area over the past many years owes an enormous debt of gratitude to Edward Witten, Andrew Hodges, and especially Freddy Cachazo and Jake Bourjaily, without whom this work would not have been possible. 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.

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Published - art_10.1007_JHEP10_2014_030.pdf

Submitted - 1312.2007v1.pdf


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