Arkani-Hamed, Nima and Bourjaily, Jacob L. and Cachazo, Freddy and Postnikov, Alexander and Trnka, Jaroslav (2015) On-Shell Structures of MHV Amplitudes Beyond the Planar Limit. Journal of High Energy Physics, 2015 (6). Art. No. 179. ISSN 1126-6708. doi:10.1007/JHEP06(2015)179. https://resolver.caltech.edu/CaltechAUTHORS:20150122-082315937
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Abstract
We initiate an exploration of on-shell functions in N = 4 SYM beyond the planar limit by providing compact, combinatorial expressions for all leading singularities of MHV amplitudes and showing that they can always be expressed as a positive sum of differently ordered Parke-Taylor tree amplitudes. This is understood in terms of an extended notion of positivity in G(2, n), the Grassmannian of 2-planes in n dimensions: a single on-shell diagram can be associated with many different “positive” regions, of which the familiar G_+(2, n) associated with planar diagrams is just one example. The decomposition into Parke-Taylor factors is simply a “triangulation” of these extended positive regions. The U(1) decoupling and Kleiss-Kuijf (KK) relations satisfied by the Parke-Taylor amplitudes also follow naturally from this geometric picture. These results suggest that non-planar MHV amplitudes in N = 4 SYM at all loop orders can be expressed as a sum of polylogarithms weighted by color factors and (unordered) Parke-Taylor amplitudes.
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Additional Information: | Open Access, © 2015 The Authors. 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: May 16, 2015; Accepted: June 8, 2015; Published: June 25, 2015. We are grateful to Andrew Hodges and Lauren Williams for helpful iscussions. N.A.-H. is supported by the Department of Energy under grant number DE-FG02-91ER40654; J.L.B. is supported by a MOBILEX grant from the Danish Council for Independent Research; F.C. is supported by the Perimeter Institute for Theoretical Physics which is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Research & Innovation; and J.T. is supported in part by the David and Ellen Lee Postdoctoral Scholarship and by the Department of Energy under grant number DE-SC0011632. | ||||||||||||||||||
Group: | Walter Burke Institute for Theoretical Physics | ||||||||||||||||||
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Subject Keywords: | Scattering Amplitudes, 1/N Expansion, Supersymmetric gauge theory | ||||||||||||||||||
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Issue or Number: | 6 | ||||||||||||||||||
DOI: | 10.1007/JHEP06(2015)179 | ||||||||||||||||||
Record Number: | CaltechAUTHORS:20150122-082315937 | ||||||||||||||||||
Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20150122-082315937 | ||||||||||||||||||
Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||||||||||
ID Code: | 53972 | ||||||||||||||||||
Collection: | CaltechAUTHORS | ||||||||||||||||||
Deposited By: | Joy Painter | ||||||||||||||||||
Deposited On: | 22 Jan 2015 21:08 | ||||||||||||||||||
Last Modified: | 10 Nov 2021 20:25 |
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