Towards the amplituhedron volume

  • Livia Ferro
  • Tomasz LukowskiEmail author
  • Andrea Orta
  • Matteo Parisi
Open Access
Regular Article - Theoretical Physics


It has been recently conjectured that scattering amplitudes in planar \( \mathcal{N}=4 \) super Yang-Mills are given by the volume of the (dual) amplituhedron. In this paper we show some interesting connections between the tree-level amplituhedron and a special class of differential equations. In particular we demonstrate how the amplituhedron volume for NMHV amplitudes is determined by these differential equations. The new formulation allows for a straightforward geometric description, without any reference to triangulations. Finally we discuss possible implications for volumes related to generic N k MHV amplitudes.


Scattering Amplitudes Extended Supersymmetry Supersymmetric gauge theory 


Open Access

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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Copyright information

© The Author(s) 2016

Authors and Affiliations

  • Livia Ferro
    • 1
  • Tomasz Lukowski
    • 2
    Email author
  • Andrea Orta
    • 1
  • Matteo Parisi
    • 1
  1. 1.Arnold-Sommerfeld-Center for Theoretical PhysicsLudwig-Maximilians-UniversitätMünchenGermany
  2. 2.Mathematical InstituteUniversity of OxfordOxfordU.K.

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