All-Helicity Symbol Alphabets from Unwound Amplituhedra

Abstract

We review an algorithm for determining the branch points of general amplitudes in planar $\mathcal{N}=4$ super-Yang-Mills theory from amplituhedra. We demonstrate how to use the recent reformulation of amplituhedra in terms of `sign flips' in order to streamline the application of this algorithm to amplitudes of any helicity. In this way we recover the known branch points of all one-loop amplitudes, and we find an `emergent positivity' on boundaries of amplituhedra.

38 pages, 5 figures, 1 big table; v2: minor corrections and improvements

References in corpus (7)

• Classical Polylogarithms for Amplitudes and Wilson Loops
• Bootstrapping a Five-Loop Amplitude Using Steinmann Relations
• Cluster adjacency properties of scattering amplitudes
• On the Singularity Structure of Maximally Supersymmetric Scattering Amplitudes
• A Cluster Bootstrap for Two-Loop MHV Amplitudes
• Stratifying On-Shell Cluster Varieties: the Geometry of Non-Planar On-Shell Diagrams
• Boundaries of Amplituhedra and NMHV Symbol Alphabets at Two Loops

Cited by in corpus (19)

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• Symbol Alphabets from Plabic Graphs
• Positive geometry, local triangulations, and the dual of the Amplituhedron
• Cluster Algebras and the Subalgebra Constructibility of the Seven-Particle Remainder Function
• Constraints on Sequential Discontinuities from the Geometry of On-shell Spaces
• Algebraic branch points at all loop orders from positive kinematics and wall crossing
• A Note on Letters of Yangian Invariants
• Symbol Alphabets from Plabic Graphs II: Rational Letters
• Sign Flip Triangulations of the Amplituhedron
• Amplituhedra, and Beyond
• Notes on polytopes, amplitudes and boundary configurations for Grassmannian string integrals
• Rooting Out Letters: Octagonal Symbol Alphabets and Algebraic Number Theory
• Internal boundaries of the loop amplituhedron
• Emergent unitarity from the amplituhedron
• Triangulation-free Trivialization of 2-loop MHV Amplituhedron