Anatomy of the amplituhedron

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

Abstract

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.

Citation

Franco, S., Galloni, D., Mariotti, A., & Trnka, J. (2015). Anatomy of the amplituhedron. Journal of High Energy Physics, 2015(3), Article 128. https://doi.org/10.1007/jhep03%282015%29128

• 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
• DOI: https://doi.org/10.1007/jhep03%282015%29128