Cluster adjacency properties of scattering amplitudes

Abstract

We conjecture a new set of analytic relations for scattering amplitudes in planar N=4 super Yang-Mills theory. They generalise the Steinmann relations and are expressed in terms of the cluster algebras associated to Gr(4,n). In terms of the symbol, they dictate which letters can appear consecutively. We study heptagon amplitudes and integrals in detail and present symbols for previously unknown integrals at two and three loops which support our conjecture.

6 pages, 3 figures. Symbols of integrals presented in four ancillary files, as detailed in README.txt

References in corpus (9)

• Gluon scattering amplitudes at strong coupling
• Classical Polylogarithms for Amplitudes and Wilson Loops
• Conformal properties of four-gluon planar amplitudes and Wilson loops
• MHV Amplitudes in N=4 Super Yang-Mills and Wilson Loops
• Hexagon Wilson loop = six-gluon MHV amplitude
• The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory
• Bootstrapping a Five-Loop Amplitude Using Steinmann Relations
• Bootstrapping an NMHV amplitude through three loops
• New differential equations for on-shell loop integrals

Cited by in corpus (63)

• Six-Gluon Amplitudes in Planar $\mathcal{N}=4$ Super-Yang-Mills Theory at Six and Seven Loops
• The Cosmic Galois Group and Extended Steinmann Relations for Planar $\mathcal{N}=4$ SYM Amplitudes
• Cluster adjacency and the four-loop NMHV heptagon
• Cluster algebras for Feynman integrals
• The Double Pentaladder Integral to All Orders
• A Three-Point Form Factor Through Five Loops
• Rationalizing Loop Integration
• Cluster adjacency beyond MHV
• Sequential Discontinuities of Feynman Integrals and the Monodromy Group
• How tropical are seven- and eight-particle amplitudes?
• Implications of the Landau Equations for Iterated Integrals
• Bootstrapping a Stress-Tensor Form Factor through Eight Loops
• Folding Amplitudes into Form Factors: An Antipodal Duality
• Lifting Heptagon Symbols to Functions
• Tropical Grassmannians, cluster algebras and scattering amplitudes
• Two-loop Octagons, Algebraic Letters and $\bar{Q}$ Equations
• All-loop singularities of scattering amplitudes in massless planar theories
• Bootstrapping two-loop Feynman integrals for planar N=4 sYM
• Singularities of eight- and nine-particle amplitudes from cluster algebras and tropical geometry
• The elliptic double box and symbology beyond polylogarithms
• Antipodal Self-Duality for a Four-Particle Form Factor
• Symbol Alphabets from the Landau Singular Locus
• Tropical fans, scattering equations and amplitudes
• Notes on cluster algebras and some all-loop Feynman integrals
• The symbol and alphabet of two-loop NMHV amplitudes from $\bar{Q}$ equations
• Truncated cluster algebras and Feynman integrals with algebraic letters
• All-Mass $n$-gon Integrals in $n$ Dimensions
• The Sklyanin Bracket and Cluster Adjacency at All Multiplicity
• Symbology for elliptic multiple polylogarithms and the symbol prime
• All-Helicity Symbol Alphabets from Unwound Amplituhedra
• Cluster Adjacency for m=2 Yangian Invariants
• Constraints on Sequential Discontinuities from the Geometry of On-shell Spaces
• Cluster Algebras and the Subalgebra Constructibility of the Seven-Particle Remainder Function
• Yangian Invariants and Cluster Adjacency in N=4 Yang-Mills
• Schubert Problems, Positivity and Symbol Letters
• Algebraic branch points at all loop orders from positive kinematics and wall crossing
• Bootstrapping elliptic Feynman integrals using Schubert analysis
• A Note on Letters of Yangian Invariants
• What can we learn about QCD and collider physics from N=4 super Yang-Mills?
• The Wilson-loop $d\log$ representation for Feynman integrals
• The Two-Loop Remainder Function for Eight and Nine Particles
• Notes on polytopes, amplitudes and boundary configurations for Grassmannian string integrals
• The Three-loop MHV Octagon from $\bar{Q}$ equations
• Rooting Out Letters: Octagonal Symbol Alphabets and Algebraic Number Theory
• The recursive structure of Baikov representations I: generics and application to symbology
• Comments on all-loop constraints for scattering amplitudes and Feynman integrals
• The SAGEX Review on Scattering Amplitudes, Chapter 5: Analytic Bootstraps for Scattering Amplitudes and Beyond
• All two-loop MHV remainder functions in multi-Regge kinematics
• Non-planar BCFW Grassmannian Geometries
• Conformally Regulated Direct Integration of the Two-Loop Heptagon Remainder
• Bootstrapping octagons in reduced kinematics from $A_2$ cluster algebras
• The m=2 amplituhedron and the hypersimplex: signs, clusters, triangulations, Eulerian numbers
• One-loop integrand from generalised scattering equations
• A Novel Algorithm for Nested Summation and Hypergeometric Expansions
• Heptagon Functions and Seven-Gluon Amplitudes in Multi-Regge Kinematics
• The Steinmann Cluster Bootstrap for N=4 Super Yang-Mills Amplitudes
• A Note on One-loop Cluster Adjacency in N = 4 SYM
• BCFW tilings and cluster adjacency for the amplituhedron
• Hierarchies in relative Picard-Lefschetz theory
• Weak Separation, Positivity and Extremal Yangian Invariants
• Combinatorial model for m-cluster categories in type E
• Species-theoretic foundations of perturbative quantum field theory
• Hexagon Bootstrap in the Double Scaling Limit