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.

34 pages, 16 figures; v2: minor corrections and improvements

References in corpus (6)

• Classical Polylogarithms for Amplitudes and Wilson Loops
• The All-Loop Integrand For Scattering Amplitudes in Planar N=4 SYM
• Bootstrapping a Five-Loop Amplitude Using Steinmann Relations
• Bootstrapping an NMHV amplitude through three loops
• A Cluster Bootstrap for Two-Loop MHV Amplitudes
• The Amplituhedron from Momentum Twistor Diagrams

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