Dual Superconformal Invariance, Momentum Twistors and Grassmannians

Abstract

Dual superconformal invariance has recently emerged as a hidden symmetry of planar scattering amplitudes in N=4 super Yang-Mills theory. This symmetry can be made manifest by expressing amplitudes in terms of `momentum twistors', as opposed to the usual twistors that make the ordinary superconformal properties manifest. The relation between momentum twistors and on-shell momenta is algebraic, so the translation procedure does not rely on any choice of space-time signature. We show that tree amplitudes and box coefficients are succinctly generated by integration of holomorphic delta-functions in momentum twistors over cycles in a Grassmannian. This is analogous to, although distinct from, recent results obtained by Arkani-Hamed et al. in ordinary twistor space. We also make contact with Hodges' polyhedral representation of NMHV amplitudes in momentum twistor space.

1+36 pages, 7 figures. Minor typos corrected

References in corpus (26)

• Gluon scattering amplitudes at strong coupling
• Conformal properties of four-gluon planar amplitudes and Wilson loops
• MHV Amplitudes in N=4 Super Yang-Mills and Wilson Loops
• Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory
• Hexagon Wilson loop = six-gluon MHV amplitude
• The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory
• Dual Superconformal Symmetry from AdS5 x S5 Superstring Integrability
• A note on dual superconformal symmetry of the N=4 super Yang-Mills S-matrix
• Null polygonal Wilson loops and minimal surfaces in Anti-de-Sitter space
• The Grassmannian Origin Of Dual Superconformal Invariance
• The S-Matrix in Twistor Space
• All tree-level amplitudes in N=4 SYM
• Exacting N=4 Superconformal Symmetry
• Sharpening The Leading Singularity
• Leading Singularities of the Two-Loop Six-Particle MHV Amplitude
• Three-Loop Leading Singularities and BDS Ansatz for Five Particles
• Tree-Level Amplitudes in N=8 Supergravity
• Dual conformal symmetry of 1-loop NMHV amplitudes in N=4 SYM theory
• On the structure of scattering amplitudes in N=4 super Yang-Mills and N=8 supergravity
• One-Loop Amplitudes in N=4 Super Yang-Mills and Anomalous Dual Conformal Symmetry
• Symmetries of the N=4 SYM S-matrix
• Twistor transform of all tree amplitudes in N=4 SYM theory
• Twistor diagram recursion for all gauge-theoretic tree amplitudes
• Scattering amplitudes for eight gauge fields
• The two-loop MHV amplitudes in N=4 supersymmetric Yang-Mills theory
• Supersymmetric Yang-Mills and Supergravity Amplitudes at One Loop

Cited by in corpus (210)

• The Amplituhedron
• The All-Loop Integrand For Scattering Amplitudes in Planar N=4 SYM
• Local Integrals for Planar Scattering Amplitudes
• The Complete Planar S-matrix of N=4 SYM as a Wilson Loop in Twistor Space
• Motivic Amplitudes and Cluster Coordinates
• Towards a Basis for Planar Two-Loop Integrals
• Five-Point Amplitudes in N=4 Super-Yang-Mills Theory and N=8 Supergravity
• Analytic result for the two-loop six-point NMHV amplitude in N=4 super Yang-Mills theory
• The Grassmannian Origin Of Dual Superconformal Invariance
• Bootstrapping an NMHV amplitude through three loops
• Heptagons from the Steinmann Cluster Bootstrap
• Notes on the scattering amplitude / Wilson loop duality
• Jumpstarting the all-loop S-matrix of planar N=4 super Yang-Mills
• Analytic form of the two-loop planar five-gluon all-plus-helicity amplitude in QCD
• Pentagon functions for massless planar scattering amplitudes
• Unification of Residues and Grassmannian Dualities
• The super-correlator/super-amplitude duality: Part I
• Six-Gluon Amplitudes in Planar $\mathcal{N}=4$ Super-Yang-Mills Theory at Six and Seven Loops
• On the Integrand-Reduction Method for Two-Loop Scattering Amplitudes
• The Cosmic Galois Group and Extended Steinmann Relations for Planar $\mathcal{N}=4$ SYM Amplitudes
• The Yangian origin of the Grassmannian integral
• Amplitudes and Correlators to Ten Loops Using Simple, Graphical Bootstraps
• Yangians, Grassmannians and T-duality
• One-Loop Superconformal and Yangian Symmetries of Scattering Amplitudes in N=4 Super Yang-Mills
• Evidence for a Nonplanar Amplituhedron
• All tree-level amplitudes in massless QCD
• Tree-level Amplitudes in the Nonlinear Sigma Model
• Yangian Invariant Scattering Amplitudes in Supersymmetric Chern-Simons Theory
• Generic multiloop methods and application to N=4 super-Yang-Mills
• New differential equations for on-shell loop integrals
• Recursion Relations for AdS/CFT Correlators
• Prescriptive Unitarity
• OPE for all Helicity Amplitudes
• A Note on Polytopes for Scattering Amplitudes
• Scattering Amplitudes and Wilson Loops in Twistor Space
• The Momentum Amplituhedron
• Cluster adjacency and the four-loop NMHV heptagon
• Dual Conformal Properties of Six-Dimensional Maximal Super Yang-Mills Amplitudes
• The super-correlator/super-amplitude duality: Part II
• A Proof of the Supersymmetric Correlation Function / Wilson Loop Correspondence
• Four-point correlation function of stress-energy tensors in N=4 superconformal theories
• Solution to the Ward Identities for Superamplitudes
• Superconformal invariants for scattering amplitudes in N=4 SYM theory
• Twistor-Strings, Grassmannians and Leading Singularities
• MHV Diagrams in Momentum Twistor Space
• Local Integrand Representations of All Two-Loop Amplitudes in Planar SYM
• Harmonic R-matrices for Scattering Amplitudes and Spectral Regularization
• The Double Pentaladder Integral to All Orders
• Local Spacetime Physics from the Grassmannian
• Cluster adjacency beyond MHV
• General properties of multiparton webs: proofs from combinatorics
• Nonsinglet pentagons and NMHV amplitudes
• Gravity in Twistor Space and its Grassmannian Formulation
• Yang-Baxter operators and scattering amplitudes in $\mathcal{N}=4$ super-Yang-Mills theory
• Twistor theory at fifty: from contour integrals to twistor strings
• Simple loop integrals and amplitudes in N=4 SYM
• On-shell Diagrams, Graßmannians and Integrability for Form Factors
• Spectral Parameters for Scattering Amplitudes in N=4 Super Yang-Mills Theory
• Y-system for form factors at strong coupling in AdS5 and with multi-operator insertions in AdS3
• Fermionic pentagons and NMHV hexagon
• Twistor Strings for N=8 Supergravity
• Gravity On-shell Diagrams
• On NMHV form factors in N=4 SYM theory from generalized unitarity
• The Amplituhedron from Momentum Twistor Diagrams
• Towards the Amplituhedron Volume
• A "Twistor String" Inspired Formula For Tree-Level Scattering Amplitudes in N=8 SUGRA
• Lifting Heptagon Symbols to Functions
• The Grassmannian and the Twistor String: Connecting All Trees in N=4 SYM
• Fundamental BCJ Relation in N=4 SYM From The Connected Formulation
• Two-loop Octagons, Algebraic Letters and $\bar{Q}$ Equations
• The Six-Point NMHV amplitude in Maximally Supersymmetric Yang-Mills Theory
• Unraveling L_{n,k}: Grassmannian Kinematics
• Bethe Ansatz for Yangian Invariants: Towards Super Yang-Mills Scattering Amplitudes
• A First Course on Twistors, Integrability and Gluon Scattering Amplitudes
• From dlogs to dilogs; the super Yang-Mills MHV amplitude revisited
• MHV diagrams in twistor space and the twistor action
• From the Holomorphic Wilson Loop to `d log' Loop-Integrands of Super-Yang-Mills Amplitudes
• Susy Theories and QCD: Numerical Approaches
• Stratifying On-Shell Cluster Varieties: the Geometry of Non-Planar On-Shell Diagrams
• Positroids, Plabic Graphs, and Scattering Amplitudes in Mathematica
• On Form Factors in N=4 SYM Theory and Polytopes
• The Amplituhedron and the One-loop Grassmannian Measure
• Composite Operators in the Twistor Formulation of $\mathcal{N}=4$ SYM Theory
• Bonus Yangian Symmetry for the Planar S-Matrix of N=4 Super Yang-Mills
• Generating All Tree Amplitudes in N=4 SYM by Inverse Soft Limit
• Multi-Parton Scattering Amplitudes via On-Shell Methods
• Efficient Tree-Amplitudes in N=4: Automatic BCFW Recursion in Mathematica
• N=4 Scattering Amplitudes and the Deformed Grassmannian
• Grassmannians for scattering amplitudes in 4d $\mathcal{N}=4$ SYM and 3d ABJM
• Descent equations for superamplitudes
• All Tree-Level MHV Form Factors in $\mathcal{N}=4$ SYM from Twistor Space
• Integrable Amplitude Deformations for N=4 Super Yang-Mills and ABJM Theory
• Symbol Alphabets from Plabic Graphs
• The symbol and alphabet of two-loop NMHV amplitudes from $\bar{Q}$ equations
• A dictionary between R-operators, on-shell graphs and Yangian algebras
• The SAGEX Review on Scattering Amplitudes, Chapter 8: Half BPS correlators
• Amplitudes at Infinity
• Holomorphic Linking, Loop Equations and Scattering Amplitudes in Twistor Space
• On Twistors and Conformal Field Theories from Six Dimensions
• On factorization of multiparticle pentagons
• Manifestly Dual-Conformal Loop Integration
• Amplitudes at Weak Coupling as Polytopes in AdS_5
• A Grassmannian Etude in NMHV Minors
• Amplitudes of 3d Yang Mills Theory
• Exact Superconformal and Yangian Symmetry of Scattering Amplitudes
• Positive geometry, local triangulations, and the dual of the Amplituhedron
• Dual conformal invariance for form factors
• Bootstrapping correlation functions in N=4 SYM
• On Soft Theorems And Form Factors In N=4 SYM Theory
• Cluster Adjacency for m=2 Yangian Invariants
• Correlation functions, null polygonal Wilson loops, and local operators
• Non-Chiral S-Matrix of N=4 Super Yang-Mills
• Yangian Invariants and Cluster Adjacency in N=4 Yang-Mills
• On Form Factors and Correlation Functions in Twistor Space
• Form factor recursion relations at loop level
• Bootstrapping elliptic Feynman integrals using Schubert analysis
• What can we learn about QCD and collider physics from N=4 super Yang-Mills?
• A simple collinear limit of scattering amplitudes at strong coupling
• The Geometry of On-Shell Diagrams
• Bootstrapping a Two-Loop Four-Point Form Factor
• Inverse Soft Factors and Grassmannian Residues
• Grassmannians and form factors with $q^2=0$ in N=4 SYM theory
• Twistor actions for gauge theory and gravity
• A first look at the function space for planar two-loop six-particle Feynman integrals
• Wilson lines, Grassmannians and Gauge Invariant Off-shell Amplitudes in N=4 SYM
• QCD gluon vertices from the string-inspired formalism
• An Elliptic Yangian-Invariant, `Leading Singularity'
• Null Polygonal Wilson Loops in Full N=4 Superspace
• Cross-Order Integral Relations from Maximal Cuts
• Symbol Alphabets from Plabic Graphs II: Rational Letters
• MHV Diagrams from an All-Line Recursion Relation
• Hidden Simplicity of Gauge Theory Amplitudes
• Amplituhedra, and Beyond
• Manifest colour-kinematics duality and double-copy in the string-based formalism
• Review of AdS/CFT Integrability, Chapter V.1: Scattering Amplitudes - a Brief Introduction
• Rooting Out Letters: Octagonal Symbol Alphabets and Algebraic Number Theory
• Towards the Gravituhedron: New Expressions for NMHV Gravity Amplitudes
• Spinor frame formalism for amplitudes and constrained superamplitudes of 10D SYM and 11D supergravity
• Higher loop mixed correlators in N=4 SYM
• The Three-loop MHV Octagon from $\bar{Q}$ equations
• On-shell diagrams and the geometry of planar N < 4 SYM theories
• Four dimensional ambitwistor strings and form factors of local and Wilson line operators
• Positroid Stratification of Orthogonal Grassmannian and ABJM Amplitudes
• Global Poles of the Two-Loop Six-Point N=4 SYM integrand
• On-shell diagrammatics and the perturbative structure of planar gauge theories
• One-Loop Soft Theorems via Dual Superconformal Symmetry
• Dual-Conformal Regularization of Infrared Loop Divergences and the Chiral Box Expansion
• Internal boundaries of the loop amplituhedron
• Wilson Loop Duality and OPE for Super Form Factors of Half-BPS Operators
• The Grassmannian for Celestial Superamplitudes
• Positivity Sectors and the Amplituhedron
• Yangian Symmetry for the Tree Amplituhedron
• On the Classification of Residues of the Grassmannian
• Yangian Algebra and Correlation Functions in Planar Gauge Theories
• Multi-Particle Amplitudes from the Four-Point Correlator in Planar N=4 SYM
• Correlation functions of the chiral stress-tensor multiplet in N=4 SYM
• On the Geometry of Null Polygons in Full N=4 Superspace
• Scattering amplitudes at strong coupling for 4K gluons
• Twistor fishnets
• One-loop same helicity YM amplitudes from BG currents
• Yangian in the Twistor String
• Uplifting Amplitudes in Special Kinematics
• The four-loop six-gluon NMHV ratio function
• Non-planar BCFW Grassmannian Geometries
• Multichannel conformal blocks for scattering amplitudes
• One-loop N = 4 super Yang-Mills scattering amplitudes in d dimensions, relation to open strings and polygonal Wilson loops
• A Note on Dual MHV Diagrams in N=4 SYM
• $\mathcal{N}=7$ On-Shell Diagrams and Supergravity Amplitudes in Momentum Twistor Space
• ABJM Amplitudes in U-gauge and a Soft Theorem
• Tree-level scattering amplitudes from the amplituhedron
• Non-Planar On-Shell Diagrams
• Grassmannian Integral for General Gauge Invariant Off-shell Amplitudes in N=4 SYM
• Emergent unitarity from the amplituhedron
• Yangian Symmetry in N=4 super Yang-Mills
• Integrability of N = 6 Chern-Simons Theory
• Poles At Infinity in On-shell Diagrams
• Integration-by-parts identities from the viewpoint of differential geometry
• A nice two-loop next-to-next-to-MHV amplitude in $\mathcal{N}=4$ super-Yang-Mills
• A note on generalized hypergeometric functions, KZ solutions, and gluon amplitudes
• On polarized scattering equations for superamplitudes of 11D supergravity and ambitwistor superstring
• A cluster of results on amplituhedron tiles
• On All-loop Integrands of Scattering Amplitudes in Planar N=4 SYM
• Anatomy of the Amplituhedron
• Permutation Relations of Yangian Invariants, Unitarity Cuts, and Scattering Amplitudes
• Dual conformal constraints and infrared equations from global residue theorems in N=4 SYM theory
• Deciphering the Maximal Transcendentality Principle via Bootstrap
• Heptagon Functions and Seven-Gluon Amplitudes in Multi-Regge Kinematics
• Polylogarithm identities, cluster algebras and the N=4 supersymmetric theory
• Local integrands for the five-point amplitude in planar N=4 SYM up to five loops
• Twistor and Polytope Interpretations for Subleading Color One-Loop Amplitudes
• Logarithmic Singularities and Maximally Supersymmetric Amplitudes
• A Note on One-loop Cluster Adjacency in N = 4 SYM
• Grassmannian Integrals as Matrix Models for Non-Compact Yangian Invariants
• Nonplanar On-shell Diagrams and Leading Singularities of Scattering Amplitudes
• Ambitwistor strings and reggeon amplitudes in N=4 SYM
• Generating MHV super-vertices in light-cone gauge
• Descent equation for superloop and cyclicity of OPE
• Differential equations for multi-loop integrals and two-dimensional kinematics
• Yangian symmetry of light-like Wilson loops
• Locally Finite Observables in sYM
• Grassmannian Integrals in Minkowski Signature, Amplitudes, and Integrability
• Weak Separation, Positivity and Extremal Yangian Invariants
• Perturbative Methods for Superconformal Quantum Field Theories in String - Gauge Theory Dualities
• Higher Codimension Singularities Constructing Yang-Mills Tree Amplitudes
• Twistor Parametrization of Locally BPS Super-Wilson Loops
• On the Integrable Structure of Super Yang-Mills Scattering Amplitudes
• Logarithms and Volumes of Polytopes
• On-shell Methods for Form Factors in N=4 SYM and Their Applications
• Gravity Amplitudes from a Gaussian Matrix Model
• Fourier transform from momentum space to twistor space