Landau Singularities from the Amplituhedron

Abstract

We propose a simple geometric algorithm for determining the complete set of branch points of amplitudes in planar N=4 super-Yang-Mills theory directly from the amplituhedron, without resorting to any particular representation in terms of local Feynman integrals. This represents a step towards translating integrands directly into integrals. In particular, the algorithm provides information about the symbol alphabets of general amplitudes. We illustrate the algorithm applied to the one- and two-loop MHV amplitudes.

arXiv comment34 pages, 16 figures; v2: minor corrections and improvements

References in corpus (27)

• One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits
• Fusing Gauge Theory Tree Amplitudes Into Loop Amplitudes
• Classical Polylogarithms for Amplitudes and Wilson Loops
• The Amplituhedron
• The All-Loop Integrand For Scattering Amplitudes in Planar N=4 SYM
• Local Integrals for Planar Scattering Amplitudes
• Progress in One-Loop QCD Computations
• Bootstrapping the three-loop hexagon
• Motivic Amplitudes and Cluster Coordinates
• Bootstrapping a Five-Loop Amplitude Using Steinmann Relations
• Bootstrapping an NMHV amplitude through three loops
• Into the Amplituhedron
• Superconformal symmetry and two-loop amplitudes in planar N=4 super Yang-Mills
• A Symbol of Uniqueness: The Cluster Bootstrap for the 3-Loop MHV Heptagon
• Hexagon functions and the three-loop remainder function
• The four-loop remainder function and multi-Regge behavior at NNLLA in planar N=4 super-Yang-Mills theory
• Pulling the straps of polygons
• Positive Amplitudes In The Amplituhedron
• Evidence for a Nonplanar Amplituhedron
• From multiple unitarity cuts to the coproduct of Feynman integrals
• Local Integrand Representations of All Two-Loop Amplitudes in Planar SYM
• A Cluster Bootstrap for Two-Loop MHV Amplitudes
• The Amplituhedron from Momentum Twistor Diagrams
• Landau Singularities and Symbology: One- and Two-loop MHV Amplitudes in SYM Theory
• Towards the Amplituhedron Volume
• From dlogs to dilogs; the super Yang-Mills MHV amplitude revisited
• The Amplituhedron and the One-loop Grassmannian Measure

Cited by in corpus (26)

• Unwinding the Amplituhedron in Binary
• Crossing Symmetry in the Planar Limit
• Implications of the Landau Equations for Iterated Integrals
• Cutting Deep Into The Amplituhedron
• All-loop singularities of scattering amplitudes in massless planar theories
• Bootstrapping two-loop Feynman integrals for planar N=4 sYM
• What is the $i\epsilon$ for the S-matrix?
• Boundaries of Amplituhedra and NMHV Symbol Alphabets at Two Loops
• 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
• A study of Feynman integrals with uniform transcendental weights and the symbology from dual conformal symmetry
• A Note on Letters of Yangian Invariants
• Symbol Alphabets from Plabic Graphs II: Rational Letters
• Sign Flip Triangulations of the Amplituhedron
• Amplituhedra, and Beyond
• Rooting Out Letters: Octagonal Symbol Alphabets and Algebraic Number Theory
• Towards the Gravituhedron: New Expressions for NMHV Gravity Amplitudes
• Exposing the threshold structure of loop integrals
• Towards Analytic Structure of Feynman Parameter Integrals with Rational Curves
• Internal boundaries of the loop amplituhedron
• Emergent unitarity from the amplituhedron
• The twistor Wilson loop and the amplituhedron
• Generalized unitarity method for unstable particles