Boundaries of Amplituhedra and NMHV Symbol Alphabets at Two Loops

Abstract

In this sequel to arXiv:1711.11507 we classify the boundaries of amplituhedra relevant for determining the branch points of general two-loop amplitudes in planar $\mathcal{N}=4$ super-Yang-Mills theory. We explain the connection to on-shell diagrams, which serves as a useful cross-check. We determine the branch points of all two-loop NMHV amplitudes by solving the Landau equations for the relevant configurations and are led thereby to a conjecture for the symbol alphabets of all such amplitudes.

42 pages, 6 figures, 8 tables; v2: minor corrections and improvements

References in corpus (6)

• Gluon scattering amplitudes at strong coupling
• Classical Polylogarithms for Amplitudes and Wilson Loops
• Bootstrapping a Five-Loop Amplitude Using Steinmann Relations
• The Elliptic Double-Box Integral: Massless Amplitudes Beyond Polylogarithms
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Cited by in corpus (24)

• How tropical are seven- and eight-particle amplitudes?
• Implications of the Landau Equations for Iterated Integrals
• Crossing Symmetry in the Planar Limit
• Tropical Grassmannians, cluster algebras and scattering amplitudes
• Two-loop Octagons, Algebraic Letters and $\bar{Q}$ Equations
• Bootstrapping two-loop Feynman integrals for planar N=4 sYM
• All-loop singularities of scattering amplitudes in massless planar theories
• Singularities of eight- and nine-particle amplitudes from cluster algebras and tropical geometry
• The symbol and alphabet of two-loop NMHV amplitudes from $\bar{Q}$ equations
• Symbol Alphabets from Plabic Graphs
• The seven-gluon amplitude in multi-Regge kinematics beyond leading logarithmic accuracy
• The Sklyanin Bracket and Cluster Adjacency at All Multiplicity
• All-Helicity Symbol Alphabets from Unwound Amplituhedra
• Positive geometry, local triangulations, and the dual of the Amplituhedron
• Constraints on Sequential Discontinuities from the Geometry of On-shell Spaces
• Schubert Problems, Positivity and Symbol Letters
• Algebraic branch points at all loop orders from positive kinematics and wall crossing
• Symbol Alphabets from Plabic Graphs II: Rational Letters
• Amplituhedra, and Beyond
• Sign Flip Triangulations of the Amplituhedron
• Towards the Gravituhedron: New Expressions for NMHV Gravity Amplitudes
• Notes on polytopes, amplitudes and boundary configurations for Grassmannian string integrals
• Emergent unitarity from the amplituhedron
• Triangulation-free Trivialization of 2-loop MHV Amplituhedron