Six-Gluon Amplitudes in Planar $\mathcal{N}=4$ Super-Yang-Mills Theory at Six and Seven Loops

Abstract

We compute the six-particle maximally-helicity-violating (MHV) and next-to-MHV (NMHV) amplitudes in planar maximally supersymmetric Yang-Mills theory through seven loops and six loops, respectively, as an application of the extended Steinmann relations and using the cosmic Galois coaction principle. Starting from a minimal space of functions constructed using these principles, we identify the amplitude by matching its symmetries and predicted behavior in various kinematic limits. Through five loops, the MHV and NMHV amplitudes are uniquely determined using only the multi-Regge and leading collinear limits. Beyond five loops, the MHV amplitude requires additional data from the kinematic expansion around the collinear limit, which we obtain from the Pentagon Operator Product Expansion, and in particular from its single-gluon bound state contribution. We study the MHV amplitude in the self-crossing limit, where its singular terms agree with previous predictions. Analyzing and plotting the amplitudes along various kinematical lines, we continue to find remarkable stability between loop orders.

arXiv comment51 pages, 9 figures, 1 table; v2: minor typo corrections, version to appear in JHEP

References in corpus (88)

• Harmonic Polylogarithms
• Gluon scattering amplitudes at strong coupling
• Iteration of Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory at Three Loops and Beyond
• Transcendentality and Crossing
• Classical Polylogarithms for Amplitudes and Wilson Loops
• 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
• What is the Simplest Quantum Field Theory?
• Magic identities for conformal four-point integrals
• The All-Loop Integrand For Scattering Amplitudes in Planar N=4 SYM
• The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory
• Comments on gluon scattering amplitudes via AdS/CFT
• 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
• From polygons and symbols to polylogarithmic functions
• Space-time S-matrix and Flux-tube S-matrix at Finite Coupling
• Bootstrapping the three-loop hexagon
• Hopf algebras, coproducts and symbols: an application to Higgs boson amplitudes
• Motivic Amplitudes and Cluster Coordinates
• Bootstrapping a Five-Loop Amplitude Using Steinmann Relations
• Thermodynamic Bubble Ansatz
• Harmonic Sums and Polylogarithms Generated by Cyclotomic Polynomials
• The Two-Loop Hexagon Wilson Loop in N = 4 SYM
• 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
• Into the Amplituhedron
• 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
• Generating Tree Amplitudes in N=4 SYM and N=8 SG
• 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
• N=4 supersymmetric Yang Mills scattering amplitudes at high energies: the Regge cut contribution
• Pulling the straps of polygons
• Single-valued harmonic polylogarithms and the multi-Regge limit
• The Elliptic Double-Box Integral: Massless Amplitudes Beyond Polylogarithms
• Non-MHV Tree Amplitudes in Gauge Theory
• Space-time S-matrix and Flux-tube S-matrix III. The two-particle contributions
• Traintracks Through Calabi-Yaus: Amplitudes Beyond Elliptic Polylogarithms
• A (Bounded) Bestiary of Feynman Integral Calabi-Yau Geometries
• High energy scattering in QCD and cross singularities of Wilson loops
• Cluster adjacency properties of scattering amplitudes
• Space-time S-matrix and Flux-tube S-matrix IV. Gluons and Fusion
• Exciting the GKP string at any coupling
• Multi-Regge kinematics and the moduli space of Riemann spheres with marked points
• BFKL equation for the adjoint representation of the gauge group in the next-to-leading approximation at N=4 SUSY
• OPE for all Helicity Amplitudes
• Cluster adjacency and the four-loop NMHV heptagon
• Adjoint BFKL at finite coupling: a short-cut from the collinear limit
• The Soft-Collinear Bootstrap: N=4 Yang-Mills Amplitudes at Six and Seven Loops
• The Galois coaction on ${\varphi }^4$ periods
• On the collinear limit of scattering amplitudes at strong coupling
• The Double Pentaladder Integral to All Orders
• A Cluster Bootstrap for Two-Loop MHV Amplitudes
• Local Spacetime Physics from the Grassmannian
• Cluster adjacency beyond MHV
• Rationalizing Loop Integration
• Mellin Amplitudes for Dual Conformal Integrals
• Hexagonal Wilson Loops in Planar $\mathcal{N}=4$ SYM Theory at Finite Coupling
• OPE for all Helicity Amplitudes II. Form Factors and Data Analysis
• Nonsinglet pentagons and NMHV amplitudes
• Fermionic pentagons and NMHV hexagon
• Hexagon Wilson Loop OPE and Harmonic Polylogarithms
• Multi-Loop Positivity of the Planar $\mathcal{N}=4$ SYM Six-Point Amplitude
• New Dual Conformally Invariant Off-Shell Integrals
• From dlogs to dilogs; the super Yang-Mills MHV amplitude revisited
• From the Holomorphic Wilson Loop to `d log' Loop-Integrands of Super-Yang-Mills Amplitudes
• The Differential of All Two-Loop MHV Amplitudes in N=4 Yang-Mills Theory
• The Multi-Regge limit of NMHV Amplitudes in N=4 SYM Theory
• Hexagon OPE Resummation and Multi-Regge Kinematics
• Evaluating the 6-point Remainder Function Near the Collinear Limit
• The seven-gluon amplitude in multi-Regge kinematics beyond leading logarithmic accuracy
• On factorization of multiparticle pentagons
• The Sklyanin Bracket and Cluster Adjacency at All Multiplicity
• Matrix pentagons
• Cluster Algebras and the Subalgebra Constructibility of the Seven-Particle Remainder Function
• Null Wilson loops with a self-crossing and the Wilson loop/amplitude conjecture
• Wilson loop remainder function for null polygons in the limit of self-crossing
• Hexagon remainder function in the limit of self-crossing up to three loops

Cited by in corpus (93)

• Collider Physics at the Precision Frontier
• The Cosmic Galois Group and Extended Steinmann Relations for Planar $\mathcal{N}=4$ SYM Amplitudes
• Constructing d-log integrands and computing master integrals for three-loop four-particle scattering
• Two-Loop Integrals for Planar Five-Point One-Mass Processes
• Cluster algebras for Feynman integrals
• Embedding Feynman Integral (Calabi-Yau) Geometries in Weighted Projective Space
• Structure of two-loop SMEFT anomalous dimensions via on-shell methods
• Subleading Power Resummation of Rapidity Logarithms: The Energy-Energy Correlator in $\mathcal{N}=4$ SYM
• A Three-Point Form Factor Through Five Loops
• The Origin of the Six-Gluon Amplitude in Planar $\mathcal{N}=4$ SYM
• An $S$-Matrix for Massless Particles
• Landau Discriminants
• Sequential Discontinuities of Feynman Integrals and the Monodromy Group
• Integration-by-parts reductions of Feynman integrals using Singular and GPI-Space
• Three Point Energy Correlators in the Collinear Limit: Symmetries, Dualities and Analytic Results
• How tropical are seven- and eight-particle amplitudes?
• Implications of the Landau Equations for Iterated Integrals
• Amplitudes meet Cosmology: A (Scalar) Primer
• Bootstrapping a Stress-Tensor Form Factor through Eight Loops
• Folding Amplitudes into Form Factors: An Antipodal Duality
• Lifting Heptagon Symbols to Functions
• Two-loop Octagons, Algebraic Letters and $\bar{Q}$ Equations
• Two-loop leading-colour QCD helicity amplitudes for two-photon plus jet production at the LHC
• Steinmann Relations and the Wavefunction of the Universe
• Soft gluon emission at two loops in full color
• All-order amplitudes at any multiplicity in the multi-Regge limit
• Singularities of eight- and nine-particle amplitudes from cluster algebras and tropical geometry
• The elliptic double box and symbology beyond polylogarithms
• All-Multiplicity Non-Planar MHV Amplitudes in sYM at Two Loops
• Prescriptive Unitarity for Non-Planar Six-Particle Amplitudes at Two Loops
• Antipodal Self-Duality for a Four-Particle Form Factor
• 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
• Multi-Regge Limit of the Two-Loop Five-Point Amplitudes in $\mathcal{N}=4$ Super Yang-Mills and $\mathcal{N}=8$ Supergravity
• Bootstrapping $\mathcal{N}=4$ sYM correlators using integrability
• Manifestly Dual-Conformal Loop Integration
• All-Mass $n$-gon Integrals in $n$ Dimensions
• Symbology for elliptic multiple polylogarithms and the symbol prime
• Yangian Invariants and Cluster Adjacency in N=4 Yang-Mills
• 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
• Climbing three-Reggeon ladders: four-loop amplitudes in the high-energy limit in full colour
• What can we learn about QCD and collider physics from N=4 super Yang-Mills?
• A Note on Letters of Yangian Invariants
• Bootstrapping elliptic Feynman integrals using Schubert analysis
• Feynman Integrals and Scattering Amplitudes from Wilson Loops
• The Full Color Two-Loop Six-Gluon All-Plus Helicity Amplitude
• Bootstrapping a Two-Loop Four-Point Form Factor
• The Two-Loop Remainder Function for Eight and Nine Particles
• Intersection theory rules symbology
• Renormalization and non-renormalization of scalar EFTs at higher orders
• An $n$-point QCD two-loop amplitude
• EFT matching from analyticity and unitarity
• Rooting Out Letters: Octagonal Symbol Alphabets and Algebraic Number Theory
• The Three-loop MHV Octagon from $\bar{Q}$ equations
• Anomalous Dimensions from Soft Regge Constants
• An Infinite Family of Elliptic Ladder Integrals
• Transforming the Bootstrap: Using Transformers to Compute Scattering Amplitudes in Planar N = 4 Super Yang-Mills Theory
• Towards Analytic Structure of Feynman Parameter Integrals with Rational Curves
• Comments on all-loop constraints for scattering amplitudes and Feynman integrals
• Gravity loop integrands from the ultraviolet
• The SAGEX Review on Scattering Amplitudes, Chapter 15: The Multi-Regge Limit
• The SAGEX Review on Scattering Amplitudes, Chapter 5: Analytic Bootstraps for Scattering Amplitudes and Beyond
• The two-loop eight-point amplitude in ABJM theory
• Conformally Regulated Direct Integration of the Two-Loop Heptagon Remainder
• Non-planar BCFW Grassmannian Geometries
• Bootstrapping octagons in reduced kinematics from $A_2$ cluster algebras
• Poles At Infinity in On-shell Diagrams
• An Origin Story for Amplitudes
• On polarized scattering equations for superamplitudes of 11D supergravity and ambitwistor superstring
• A nice two-loop next-to-next-to-MHV amplitude in $\mathcal{N}=4$ super-Yang-Mills
• Antipodal Symmetry of Two-Loop MHV Amplitudes
• A Novel Algorithm for Nested Summation and Hypergeometric Expansions
• Heptagon Functions and Seven-Gluon Amplitudes in Multi-Regge Kinematics
• Deciphering the Maximal Transcendentality Principle via Bootstrap
• A Two-Loop Four-Point Form Factor at Function Level
• Spinning Hexagons
• The two-loop Higgs impact factor
• All Two-Loop, Color-Dressed, Six-Point Amplitude Integrands in sYM
• The Multi-Regge Limit from the Wilson Loop OPE
• Locally Finite Observables in sYM
• Loop Equation and Exact Soft Anomalous Dimension in N=4 Super Yang-Mills
• Infrared and transcendental structure of two-loop supersymmetric QCD amplitudes
• Exploring Reggeon bound states in strongly-coupled $\mathcal{N}=4$ super Yang-Mills
• Analytic Four-Point Lightlike Form Factors and OPE of Null-Wrapped Polygons
• Integrands of Less-Supersymmetric Yang-Mills at One Loop
• Quark-Gluon Backscattering in the Regge Limit at One-Loop
• Universal transcendentality limit of BFKL eigenvalue
• One-loop central-emission vertex for two gluons in $\mathcal{N}=4$ super Yang-Mills theory
• Hexagon Bootstrap in the Double Scaling Limit