Amplitudes and Correlators to Ten Loops Using Simple, Graphical Bootstraps

Abstract

We introduce two new graphical-level relations among possible contributions to the four-point correlation function and scattering amplitude in planar, maximally supersymmetric Yang-Mills theory. When combined with the rung rule, these prove powerful enough to fully determine both functions through ten loops. This then also yields the full five-point amplitude to eight loops and the parity-even part to nine loops. We derive these rules, illustrate their applications, compare their relative strengths for fixing coefficients, and survey some of the features of the previously unknown nine and ten loop expressions. Explicit formulae for amplitudes and correlators through ten loops are available at: http://goo.gl/JH0yEc.

35 pages, 52 figures, and 6 tables. Complete expressions for the amplitude and correlator through ten loops can be obtained at: http://goo.gl/JH0yEc

References in corpus (44)

• Gluon scattering amplitudes at strong coupling
• Iteration of Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory at Three Loops and Beyond
• Dual superconformal symmetry of scattering amplitudes in N=4 super-Yang-Mills theory
• Conformal properties of four-gluon planar amplitudes and Wilson loops
• What is the Simplest Quantum Field Theory?
• MHV Amplitudes in N=4 Super Yang-Mills and Wilson Loops
• 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
• Local Integrals for Planar Scattering Amplitudes
• On planar gluon amplitudes/Wilson loops duality
• Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory
• Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory
• A Duality For The S Matrix
• Dual Superconformal Invariance, Momentum Twistors and Grassmannians
• A novel approach to integration by parts reduction
• Two-Loop Four-Gluon Amplitudes in N=4 Super-Yang-Mills
• The Complete Planar S-matrix of N=4 SYM as a Wilson Loop in Twistor Space
• Maximally Supersymmetric Planar Yang-Mills Amplitudes at Five Loops
• A note on dual superconformal symmetry of the N=4 super Yang-Mills S-matrix
• Scattering into the fifth dimension of N=4 super Yang-Mills
• Notes on the scattering amplitude / Wilson loop duality
• From correlation functions to Wilson loops
• Three-Loop Four-Point Correlator in N=4 SYM
• Anomalous dimensions in N=4 SYM theory at order g^4
• Unification of Residues and Grassmannian Dualities
• The super-correlator/super-amplitude duality: Part I
• From correlation functions to scattering amplitudes
• Leading singularities and off-shell conformal integrals
• Constructing the correlation function of four stress-tensor multiplets and the four-particle amplitude in N=4 SYM
• Hidden symmetry of four-point correlation functions and amplitudes in N=4 SYM
• Four-point functions in N=4 supersymmetric Yang-Mills theory at two loops
• Simplifications of four-point functions in N=4 supersymmetric Yang-Mills theory at two loops
• More on the duality correlators/amplitudes
• A note on four-point functions of conformal operators in N=4 Super-Yang Mills
• The super-correlator/super-amplitude duality: Part II
• The Soft-Collinear Bootstrap: N=4 Yang-Mills Amplitudes at Six and Seven Loops
• A Proof of the Supersymmetric Correlation Function / Wilson Loop Correspondence
• D = 5 maximally supersymmetric Yang-Mills theory diverges at six loops
• Perturbation Theory at Eight Loops: Novel Structures and the Breakdown of Manifest Conformality
• Local Integrand Representations of All Two-Loop Amplitudes in Planar SYM
• Local Spacetime Physics from the Grassmannian
• Five-loop Konishi in N=4 SYM
• Collinear and Soft Limits of Multi-Loop Integrands in N=4 Yang-Mills
• Local integrands for the five-point amplitude in planar N=4 SYM up to five loops

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• The Elliptic Double-Box Integral: Massless Amplitudes Beyond Polylogarithms
• Traintracks Through Calabi-Yaus: Amplitudes Beyond Elliptic Polylogarithms
• A (Bounded) Bestiary of Feynman Integral Calabi-Yau Geometries
• Unmixing Supergravity
• Bootstrapping the simplest correlator in planar N = 4 SYM at all loops
• Prescriptive Unitarity
• Exact properties of an integrated correlator in $\mathcal{N}=4$ $SU(N)$ SYM
• Energy-energy correlations at next-to-next-to-leading order
• Perturbative Four-Point Functions In Planar N=4 SYM From Hexagonalization
• One-loop amplitudes in $Ad{S}_5\times S^5$ supergravity from $\mathcal{N}=4$ SYM at strong coupling
• Subleading Power Resummation of Rapidity Logarithms: The Energy-Energy Correlator in $\mathcal{N}=4$ SYM
• Ten dimensional symmetry of N=4 SYM correlators
• The Correlahedron
• Cutting Deep Into The Amplituhedron
• All-Multiplicity Non-Planar MHV Amplitudes in sYM at Two Loops
• Prescriptive Unitarity for Non-Planar Six-Particle Amplitudes at Two Loops
• The SAGEX Review on Scattering Amplitudes, Chapter 8: Half BPS correlators
• All five-loop planar four-point functions of half-BPS operators in $\mathcal{N}=4$ SYM
• Amplitudes at Infinity
• Manifestly Dual-Conformal Loop Integration
• Modular-invariant large-$N$ completion of an integrated correlator in $\mathcal{N}=4$ supersymmetric Yang-Mills theory
• The SAGEX Review on Scattering Amplitudes, Chapter 10: Selected topics on modular covariance of type IIB string amplitudes and their $\mathcal{N}=4$ supersymmetric Yang-Mills duals
• Integrated correlators in $\mathcal{N}=4$ super Yang-Mills and periods
• Building Bases of Loop Integrands
• Non-planar data of $\mathcal{N}=4$ SYM
• Laplace-difference equation for integrated correlators of operators with general charges in $\mathcal{N}=4$ SYM
• All-Loop Four-Point Aharony-Bergman-Jafferis-Maldacena Amplitudes from Dimensional Reduction of the Amplituhedron
• Konishi OPE coefficient at the five loop order
• An Elliptic Yangian-Invariant, `Leading Singularity'
• Integrated negative geometries in ABJM
• Amplituhedron-like geometries
• All-loop cuts from the Amplituhedron
• Higher-Point Integrands in N=4 super Yang-Mills Theory
• Internal boundaries of the loop amplituhedron
• Multi-Particle Amplitudes from the Four-Point Correlator in Planar N=4 SYM
• Non-planar integrated correlator in $\mathcal{N}=4$ SYM
• Conformally Regulated Direct Integration of the Two-Loop Heptagon Remainder
• Non-planar BCFW Grassmannian Geometries
• 4-particle Amplituhedronics for 3-5 Loops
• Poles At Infinity in On-shell Diagrams
• Notes on conformal integrals: Coulomb branch amplitudes, magic identities and bootstrap
• All-loop Mondrian Reduction of 4-particle Amplituhedron at Positive Infinity
• Triangulation-free Trivialization of 2-loop MHV Amplituhedron
• All-loop Mondrian Diagrammatics and 4-particle Amplituhedron
• A Novel Algorithm for Nested Summation and Hypergeometric Expansions
• Amplitudes for Astrophysicists: Known Knowns
• Illustrations of Integrand-Basis Building at Two Loops
• Leading singularities and chambers of Correlahedron
• Exact expressions for $n$-point maximal $U(1{)}_Y$-violating integrated correlators in $SU(N)$ $\mathcal{N}=4$ SYM