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Anatomy of the amplituhedron

Franco, Sebastián; Galloni, Daniele; Mariotti, Alberto; Trnka, Jaroslav

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Sebastián Franco

Daniele Galloni

Alberto Mariotti

Jaroslav Trnka


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.

Journal Article Type Article
Acceptance Date Feb 28, 2015
Online Publication Date Mar 24, 2015
Publication Date Mar 24, 2015
Deposit Date Apr 9, 2019
Publicly Available Date Apr 10, 2019
Journal Journal of High Energy Physics
Print ISSN 1126-6708
Publisher Scuola Internazionale Superiore di Studi Avanzati (SISSA)
Peer Reviewed Peer Reviewed
Volume 2015
Issue 3
Article Number 128
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Copyright Statement
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.

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