All-loop cuts from the Amplituhedron

  • Cameron Langer
  • Akshay Yelleshpur SrikantEmail author
Open Access
Regular Article - Theoretical Physics


The definition of the amplituhedron in terms of sign flips involves both one-loop constraints and the “mutual positivity” constraint. To gain an understanding of the all-loop integrand of \( \mathcal{N}=4 \) sYM requires understanding the crucial role played by mutual positivity. This paper is an attempt towards developing a procedure to introduce the complexities of mutual positivity in a systematic and controlled manner. As the first step in this procedure, we trivialize these constraints and understand the geometry underlying the remaining constraints to all loops and multiplicities. We present a host of configurations which correspond to various faces of the amplituhedron. The results we derive are valid at all multiplicities and loop orders for the maximally helicity violating (MHV) configurations. These include detailed derivations for the results in [1]. We conclude by indicating how one might move beyond trivial mutual positivity by presenting a series of configuration which re-introduce it bit by bit.


Scattering Amplitudes 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) 2019

Authors and Affiliations

  1. 1.Center for Quantum Mathematics and Physics (QMAP)University of CaliforniaDavisU.S.A.
  2. 2.Department of PhysicsPrinceton UniversityPrincetonU.S.A.

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