Cluster adjacency beyond MHV

Abstract

We explore further the notion of cluster adjacency, focussing on non-MHV amplitudes. We extend the notion of adjacency to the BCFW decomposition of tree-level amplitudes. Adjacency controls the appearance of poles, both physical and spurious, in individual BCFW terms. We then discuss how this notion of adjacency is connected to the adjacency already observed at the level of symbols of scattering amplitudes which controls the appearance of branch cut singularities. Poles and symbols become intertwined by cluster adjacency and we discuss the relation of this property to the $\bar{Q}$-equation which imposes constraints on the derivatives of the transcendental functions appearing in loop amplitudes.

arXiv comment51 pages, 25 figures, 4 tables

References in corpus (50)

• Direct Proof Of Tree-Level Recursion Relation In Yang-Mills Theory
• One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits
• Harmonic Polylogarithms
• Multiloop integrals in dimensional regularization made simple
• Gluon scattering amplitudes at strong coupling
• Differential Equations for Feynman Graph Amplitudes
• Classical Polylogarithms for Amplitudes and Wilson Loops
• Dimensionally Regulated Pentagon Integrals
• Dual superconformal symmetry of scattering amplitudes in N=4 super-Yang-Mills theory
• Conformal properties of four-gluon planar amplitudes and Wilson loops
• The Amplituhedron
• Cluster algebras II: Finite type classification
• MHV Amplitudes in N=4 Super Yang-Mills and Wilson Loops
• The All-Loop Integrand For Scattering Amplitudes in Planar N=4 SYM
• Conformal Ward identities for Wilson loops and a test of the duality with gluon amplitudes
• On planar gluon amplitudes/Wilson loops duality
• Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory
• Hexagon Wilson loop = six-gluon MHV amplitude
• A Duality For The S Matrix
• The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory
• Dual Superconformal Invariance, Momentum Twistors and Grassmannians
• Space-time S-matrix and Flux-tube S-matrix at Finite Coupling
• Bootstrapping the three-loop hexagon
• The elliptic dilogarithm for the sunset graph
• Motivic Amplitudes and Cluster Coordinates
• Bootstrapping a Five-Loop Amplitude Using Steinmann Relations
• Null polygonal Wilson loops and minimal surfaces in Anti-de-Sitter space
• Analytic result for the two-loop six-point NMHV amplitude in N=4 super Yang-Mills theory
• An Operator Product Expansion for Polygonal null Wilson Loops
• Bootstrapping an NMHV amplitude through three loops
• Uniqueness of two-loop master contours
• BFKL Pomeron, Reggeized gluons and Bern-Dixon-Smirnov amplitudes
• 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
• Heptagons from the Steinmann Cluster Bootstrap
• Jumpstarting the all-loop S-matrix of planar N=4 super Yang-Mills
• Hexagon functions and the three-loop remainder function
• Space-time S-matrix and Flux tube S-matrix II. Extracting and Matching Data
• An Analytic Result for the Two-Loop Hexagon Wilson Loop in N = 4 SYM
• The four-loop remainder function and multi-Regge behavior at NNLLA in planar N=4 super-Yang-Mills theory
• The Elliptic Double-Box Integral: Massless Amplitudes Beyond Polylogarithms
• Space-time S-matrix and Flux-tube S-matrix III. The two-particle contributions
• Elliptic Feynman integrals and pure functions
• Multiple Elliptic Polylogarithms
• Traintracks Through Calabi-Yaus: Amplitudes Beyond Elliptic Polylogarithms
• Cluster adjacency properties of scattering amplitudes
• Space-time S-matrix and Flux-tube S-matrix IV. Gluons and Fusion
• Cluster adjacency and the four-loop NMHV heptagon
• Efficient Tree-Amplitudes in N=4: Automatic BCFW Recursion in Mathematica
• Descent equations for superamplitudes

Cited by in corpus (34)

• 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
• A Three-Point Form Factor Through Five Loops
• How tropical are seven- and eight-particle amplitudes?
• Lifting Heptagon Symbols to Functions
• Tropical Grassmannians, cluster algebras and scattering amplitudes
• Two-loop Octagons, Algebraic Letters and $\bar{Q}$ Equations
• The elliptic double box and symbology beyond polylogarithms
• Antipodal Self-Duality for a Four-Particle Form Factor
• Symbol Alphabets from Plabic Graphs
• Tropical fans, scattering equations and amplitudes
• 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
• Symbology for elliptic multiple polylogarithms and the symbol prime
• Cluster Adjacency for m=2 Yangian Invariants
• Yangian Invariants and Cluster Adjacency in N=4 Yang-Mills
• 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
• Bootstrapping elliptic Feynman integrals using Schubert analysis
• Rooting Out Letters: Octagonal Symbol Alphabets and Algebraic Number Theory
• The Three-loop MHV Octagon from $\bar{Q}$ equations
• Comments on all-loop constraints for scattering amplitudes and Feynman integrals
• All two-loop MHV remainder functions in multi-Regge kinematics
• Heptagon Functions and Seven-Gluon Amplitudes in Multi-Regge Kinematics
• A Novel Algorithm for Nested Summation and Hypergeometric Expansions
• 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
• Cluster Alphabets from Generalized Worldsheets: A Geometric Approach to Finite Types
• Hexagon Bootstrap in the Double Scaling Limit