Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory

Abstract

Tree-level scattering amplitudes in N=4 super Yang-Mills theory have recently been shown to transform covariantly with respect to a 'dual' superconformal symmetry algebra, thus extending the conventional superconformal symmetry algebra psu(2,2|4) of the theory. In this paper we derive the action of the dual superconformal generators in on-shell superspace and extend the dual generators suitably to leave scattering amplitudes invariant. We then study the algebra of standard and dual symmetry generators and show that the inclusion of the dual superconformal generators lifts the psu(2,2|4) symmetry algebra to a Yangian. The non-local Yangian generators acting on amplitudes turn out to be cyclically invariant due to special properties of psu(2,2|4). The representation of the Yangian generators takes the same form as in the case of local operators, suggesting that the Yangian symmetry is an intrinsic property of planar N=4 super Yang-Mills, at least at tree level.

23 pages, no figures; v2: typos corrected, references added; v3: minor changes, references added

References in corpus (21)

• 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
• The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory
• The AdS_5xS^5 superstring worldsheet S-matrix and crossing symmetry
• Hexagon Wilson loop = six-gluon MHV amplitude
• The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory
• Four-loop perturbative Konishi from strings and finite size effects for multiparticle states
• Maximally Supersymmetric Planar Yang-Mills Amplitudes at Five Loops
• Dual Superconformal Symmetry from AdS5 x S5 Superstring Integrability
• A note on dual superconformal symmetry of the N=4 super Yang-Mills S-matrix
• The hexagon Wilson loop and the BDS ansatz for the six-gluon amplitude
• All tree-level amplitudes in N=4 SYM
• Anomalous dimension with wrapping at four loops in N=4 SYM
• Strong-coupling expansion of cusp anomaly from quantum superstring
• The Classical r-matrix of AdS/CFT and its Lie Bialgebra Structure
• Recursion Relations, Generating Functions, and Unitarity Sums in N=4 SYM Theory
• A Yangian Double for the AdS/CFT Classical r-matrix
• Bound States, Yangian Symmetry and Classical r-matrix for the AdS5 x S5 Superstring
• Yangian Symmetry of Long-Range gl(N) Integrable Spin Chains
• Weakly coupled N=4 Super Yang-Mills and N=6 Chern-Simons theories from u(2|2) Yangian symmetry

Cited by in corpus (109)

• The All-Loop Integrand For Scattering Amplitudes in Planar N=4 SYM
• The Complete Planar S-matrix of N=4 SYM as a Wilson Loop in Twistor Space
• Loop Corrections to Soft Theorems in Gauge Theories and Gravity
• Notes on the scattering amplitude / Wilson loop duality
• The Complete Four-Loop Four-Point Amplitude in N=4 Super-Yang-Mills Theory
• Exacting N=4 Superconformal Symmetry
• The Yangian origin of the Grassmannian integral
• One-Loop Superconformal and Yangian Symmetries of Scattering Amplitudes in N=4 Super Yang-Mills
• Amplitudes and Correlators to Ten Loops Using Simple, Graphical Bootstraps
• All tree-level amplitudes in massless QCD
• Higgs-regularized three-loop four-gluon amplitude in N=4 SYM: exponentiation and Regge limits
• Yangian Invariant Scattering Amplitudes in Supersymmetric Chern-Simons Theory
• Multi-Regge kinematics and the moduli space of Riemann spheres with marked points
• On form factors in N=4 sym
• Spinor Helicity and Dual Conformal Symmetry in Ten Dimensions
• Four-gluon scattering at three loops, infrared structure and Regge limit
• New differential equations for on-shell loop integrals
• Dual Superconformal Symmetry of N=6 Chern-Simons Theory
• Dual Conformal Properties of Six-Dimensional Maximal Super Yang-Mills Amplitudes
• Cluster algebras for Feynman integrals
• Lectures on Yangian Symmetry
• MHV Diagrams in Momentum Twistor Space
• Harmonic R-matrices for Scattering Amplitudes and Spectral Regularization
• Conformal Anomaly for Amplitudes in N=6 Superconformal Chern-Simons Theory
• Amplitudes of 3D and 6D Maximal Superconformal Theories in Supertwistor Space
• Simple loop integrals and amplitudes in N=4 SYM
• One Loop Amplitudes In ABJM
• The Amplituhedron from Momentum Twistor Diagrams
• Yangians, S-matrices and AdS/CFT
• The Six-Point NMHV amplitude in Maximally Supersymmetric Yang-Mills Theory
• Four-graviton scattering to three loops in $\mathcal{N}=8$ supergravity
• Scattering Amplitudes in Quantum Field Theory
• Stratifying On-Shell Cluster Varieties: the Geometry of Non-Planar On-Shell Diagrams
• One-Loop Amplitudes in N=4 Super Yang-Mills and Anomalous Dual Conformal Symmetry
• Massive Conformal Symmetry and Integrability for Feynman Integrals
• Bonus Yangian Symmetry for the Planar S-Matrix of N=4 Super Yang-Mills
• T-Duality, Dual Conformal Symmetry and Integrability for Strings on AdS_5 x S^5
• Celestial Dual Superconformal Symmetry, MHV Amplitudes and Differential Equations
• N=4 Scattering Amplitudes and the Deformed Grassmannian
• Proof of the Dual Conformal Anomaly of One-Loop Amplitudes in N=4 SYM
• The symbol and alphabet of two-loop NMHV amplitudes from $\bar{Q}$ equations
• Celestial superamplitude in $\mathcal{N}=4$ SYM theory
• Manifestly Dual-Conformal Loop Integration
• Amplitudes at Weak Coupling as Polytopes in AdS_5
• Wilson loop OPE, analytic continuation and multi-Regge limit
• Conformal invariance from non-conformal gravity
• The orthogonal momentum amplituhedron and ABJM amplitudes
• Building Bases of Loop Integrands
• On the ABJM four-point amplitude at three loops and BDS exponentiation
• Yangian Bootstrap for Massive Feynman Integrals
• Celestial Superamplitudes
• What can we learn about QCD and collider physics from N=4 super Yang-Mills?
• The SAGEX Review on Scattering Amplitudes, Chapter 7: Positive Geometry of Scattering Amplitudes
• A simple collinear limit of scattering amplitudes at strong coupling
• From Six to Four and More: Massless and Massive Maximal Super Yang-Mills Amplitudes in 6d and 4d and their Hidden Symmetries
• Inverse Soft Factors and Grassmannian Residues
• Prescriptive Unitarity with Elliptic Leading Singularities
• The Wilson-loop $d\log$ representation for Feynman integrals
• A Requiem for $Ad{S}_4\times \mathbb{C}{P}^3$ Fermionic self-T-duality
• Massive Fishnets
• Cross-Order Integral Relations from Maximal Cuts
• Null Polygonal Wilson Loops in Full N=4 Superspace
• An Elliptic Yangian-Invariant, `Leading Singularity'
• Slightly Broken Higher Spin Symmetry: General Structure of Correlators
• Amplituhedra, and Beyond
• Serre Relation and Higher Grade Generators of the AdS/CFT Yangian Symmetry
• Towards the Gravituhedron: New Expressions for NMHV Gravity Amplitudes
• The Three-loop MHV Octagon from $\bar{Q}$ equations
• Yangian Ward Identities for Fishnet Four-Point Integrals
• Infrared properties of five-point massive amplitudes in N=4 SYM on the Coulomb branch
• Integrability for Feynman Integrals
• Integrability and MHV diagrams in N=4 supersymmetric Yang-Mills theory
• The Grassmannian for Celestial Superamplitudes
• On three-point functions in ABJM and the latitude Wilson loop
• Manifest SO(N) invariance and S-matrices of three-dimensional N=2,4,8 SYM
• The SAGEX Review on Scattering Amplitudes, Chapter 5: Analytic Bootstraps for Scattering Amplitudes and Beyond
• On the Geometry of Null Polygons in Full N=4 Superspace
• Correlators on the wall and ${\mathfrak{sl}}_n$ spin chain
• Non-planar BCFW Grassmannian Geometries
• Yangian in the Twistor String
• Correlators with $s{\ell }_2$ Yangian symmetry
• A Note on Dual MHV Diagrams in N=4 SYM
• Heat kernel expansion and induced action for the matrix model Dirac operator
• BCJ, worldsheet quantum algebra and KZ equations
• 6d Dual Conformal Symmetry and Minimal Volumes in AdS
• Supersymmetric Yang-Mills and Supergravity Amplitudes at One Loop
• Illustrations of Integrand-Basis Building at Two Loops
• Properties of the Conformal Yangian in Scalar and Gauge Field Theories
• Demystifying integrable QFTs in AdS: No-go theorems for higher-spin charges
• Wilson loops in N=6 superspace for ABJM theory
• Bonus scaling and BCFW in N=7 supergravity
• The Feyn-Structure of Yangian Symmetry
• Antipodal self-duality of square fishnet graphs
• From equations in coordinate space to Picard-Fuchs and back
• On hydrogen-like bound states in $\mathcal{N}=4$ super Yang-Mills
• Light-cone limits of large rectangular fishnets
• A note on NMHV form factors from the Graßmannian and the twistor string
• All Two-Loop, Color-Dressed, Six-Point Amplitude Integrands in sYM
• Grassmannian Integrals as Matrix Models for Non-Compact Yangian Invariants
• Rational Terms in Theories with Matter
• Yangian Symmetry in Five Dimensions
• Commuting Conformal and Dual Conformal Symmetries in the Regge limit
• Dual Conformal Symmetry and Iterative Integrals in Six Dimensions
• Integrands of Less-Supersymmetric Yang-Mills at One Loop
• Yangian symmetry applied to Quantum chromodynamics
• Symplectic Grassmannians, dual conformal symmetry and 4-point amplitudes in 6D
• On Exact Solvability of $\mathcal{N}$=4 super Yang-Mills
• The Aharony-Bergman-Jafferis-Maldacena theory on a circle
• Dilogarithm ladders from Wilson loops