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Anatomy of the Amplituhedron

Franco, Sebastián and Galloni, Daniele and Mariotti, Alberto and Trnka, Jaroslav (2015) Anatomy of the Amplituhedron. Journal of High Energy Physics, 2015 (3). Art. No. 128. ISSN 1126-6708. doi:10.1007/JHEP03(2015)128.

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We initiate a comprehensive investigation of the geometry of the amplituhedron, a recently found geometric object whose volume calculates the integrand of scattering amplitudes in planar N=4 SYM theory. We do so by introducing and studying its stratification, focusing on four-point amplitudes. The new stratification exhibits interesting combinatorial properties and positivity is neatly captured by permutations. As explicit examples, we find all boundaries for the two and three loop amplitudes and related geometries. We recover the stratifications of some of these geometries from the singularities of the corresponding integrands, providing a non-trivial test of the amplituhedron/scattering amplitude correspondence. We finally introduce a deformation of the stratification with remarkably simple topological properties.

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Additional Information:© 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. Received: February 3, 2015; Accepted: February 28, 2015; Published: March 24, 2015. We would like to thank N. Arkani-Hamed for very useful discussions. D. G. would like to thank the Simons Summer Workshop at the Simons Center for Geometry and Physics for hospitality during the completion of this work. The work of S. F. and D. G. is supported by the U.K. Science and Technology Facilities Council (STFC). A.M. acknowledges funding by the Durham International Junior Research Fellowship. J. T. is supported in part by the David and Ellen Lee Postdoctoral Scholarship and by DOE grant DE-FG03-92-ER40701.
Group:Walter Burke Institute for Theoretical Physics
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Science and Technology Facilities Council (STFC)UNSPECIFIED
Durham International Junior Research FellowshipUNSPECIFIED
David and Ellen Lee Postdoctoral ScholarshipUNSPECIFIED
Department of Energy (DOE)DE-FG03-92-ER40701
Subject Keywords:Supersymmetric gauge theory; Scattering Amplitudes
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Issue or Number:3
Record Number:CaltechAUTHORS:20140825-123237108
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:48850
Deposited By: Joy Painter
Deposited On:25 Aug 2014 21:27
Last Modified:10 Nov 2021 18:36

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