Cutting Deep Into The Amplituhedron

Abstract

In this letter we compute a canonical set of cuts of the integrand for MHV amplitudes in planar $\mathcal{N}=4$ SYM, 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 non-trivial results on scattering amplitudes in the theory valid for arbitrarily many loops and external particle multiplicities.

6 pages, 1 table, 6 figures

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Cited by in corpus (27)

• Nonperturbative Negative Geometries: Amplitudes at Strong Coupling and the Amplituhedron
• Accordiohedra as positive geometries for generic scalar field theories
• The SAGEX Review on Scattering Amplitudes, Chapter 8: Half BPS correlators
• On Positive Geometries of Quartic Interactions II : Stokes polytopes, Lower Forms on Associahedra and Worldsheet Forms
• Positive geometry, local triangulations, and the dual of the Amplituhedron
• The positive geometry for ${\varphi }^p$ interactions
• The SAGEX Review on Scattering Amplitudes, Chapter 7: Positive Geometry of Scattering Amplitudes
• All-Loop Four-Point Aharony-Bergman-Jafferis-Maldacena Amplitudes from Dimensional Reduction of the Amplituhedron
• Amplituhedra, and Beyond
• Sign Flip Triangulations of the Amplituhedron
• Towards the Gravituhedron: New Expressions for NMHV Gravity Amplitudes
• Multi-spin soft bootstrap and scalar-vector Galileon
• Integrated negative geometries in ABJM
• Amplituhedron-like geometries
• All-loop cuts from the Amplituhedron
• A Soft Theorem for the Tropical Grassmannian
• Gravity loop integrands from the ultraviolet
• Emergent unitarity, all-loop cuts and integrations from the ABJM amplituhedron
• Internal boundaries of the loop amplituhedron
• Triangulation of 2-loop MHV Amplituhedron from Sign Flips
• Emergent unitarity from the amplituhedron
• On the Positive Geometry of Quartic Interactions III : One Loop Integrands from Polytopes
• Triangulation-free Trivialization of 2-loop MHV Amplituhedron
• All-loop Mondrian Reduction of 4-particle Amplituhedron at Positive Infinity
• Double Soft Theorem for Generalised Biadjoint Scalar Amplitudes
• Positive Geometry for Stringy Scalar Amplitudes
• Extended DBI and its generalizations from graded soft theorems