# Deep Into the Amplituhedron: Amplitude Singularities at All Loops and Legs

Arkani-Hamed, Nima (School of Natural Sciences, Institute for Advanced Study, Princeton, New Jersey 08540, USA) ; Langer, Cameron (Center for Quantum Mathematics and Physics (QMAP), University of California, Davis, California 95616, USA) ; Srikant, Akshay Yelleshpur (Department of Physics, Princeton University, New Jersey 08544, USA) ; Trnka, Jaroslav (Center for Quantum Mathematics and Physics (QMAP), University of California, Davis, California 95616, USA)

07 February 2019

Abstract: In this Letter we compute a canonical set of cuts of the integrand for maximally helicity violating amplitudes in planar $N=4$ supersymmetric Yang-Mills theory, where all internal propagators are put on shell. These “deepest cuts” probe the most complicated Feynman diagrams and on-shell processes that can possibly contribute to the amplitude, but are also naturally associated with remarkably simple geometric facets of the amplituhedron. The recent reformulation of the amplituhedron in terms of combinatorial geometry directly in the kinematic (momentum-twistor) space plays a crucial role in understanding this geometry and determining the cut. This provides us with the first nontrivial results on scattering amplitudes in the theory valid for arbitrarily many loops and external particle multiplicities.

Published in: Physical Review Letters 122 (2019)