All tree-level amplitudes in N=4 SYM

Abstract

We give an explicit formula for all tree amplitudes in N=4 SYM, derived by solving the recently presented supersymmetric tree-level recursion relations. The result is given in a compact, manifestly supersymmetric form and we show how to extract from it all possible component amplitudes for an arbitrary number of external particles and any arrangement of external particles and helicities. We focus particularly on extracting gluon amplitudes which are valid for any gauge theory. The formula for all tree-level amplitudes is given in terms of nested sums of dual superconformal invariants and it therefore manifestly respects both conventional and dual superconformal symmetry.

26 pages. Boundary terms in sums corrected. Additional references. Acknowledgement added. Extended discussion. One new figure

References in corpus (27)

• Direct Proof Of Tree-Level Recursion Relation In Yang-Mills Theory
• New Relations for Gauge-Theory Amplitudes
• Perturbative Gauge Theory As A String Theory In Twistor Space
• New Recursion Relations for Tree Amplitudes of Gluons
• Gluon scattering amplitudes at strong coupling
• Multi-Parton Amplitudes in Gauge Theories
• MHV Vertices And Tree Amplitudes In Gauge Theory
• Conformal properties of four-gluon planar amplitudes and Wilson loops
• MHV Amplitudes in N=4 Super Yang-Mills and Wilson Loops
• Magic identities for conformal four-point integrals
• The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory
• On planar gluon amplitudes/Wilson loops duality
• Comments on gluon scattering amplitudes via AdS/CFT
• The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory
• Fermionic T-Duality, Dual Superconformal Symmetry, and the Amplitude/Wilson Loop Connection
• On Tree Amplitudes in Gauge Theory and Gravity
• 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
• Scattering Amplitudes, Wilson Loops and the String/Gauge Theory Correspondence
• The hexagon Wilson loop and the BDS ansatz for the six-gluon amplitude
• Generating Tree Amplitudes in N=4 SYM and N=8 SG
• Non-MHV Tree Amplitudes in Gauge Theory
• Next-to-Maximal Helicity Violating Amplitudes in Gauge Theory
• All Next-to-Maximally-Helicity-Violating One-Loop Gluon Amplitudes in N=4 Super-Yang-Mills Theory
• All Split Helicity Tree-Level Gluon Amplitudes
• Coplanarity In Twistor Space Of N=4 Next-To-MHV One-Loop Amplitude Coefficients

Cited by in corpus (136)

• The All-Loop Integrand For Scattering Amplitudes in Planar N=4 SYM
• Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory
• A Duality For The S Matrix
• Dual Superconformal Invariance, Momentum Twistors and Grassmannians
• Scattering into the fifth dimension of N=4 super Yang-Mills
• Analytic result for the two-loop six-point NMHV amplitude in N=4 super Yang-Mills theory
• Notes on the scattering amplitude / Wilson loop duality
• The S-Matrix in Twistor Space
• Pure Gravities via Color-Kinematics Duality for Fundamental Matter
• Color-Kinematics Duality for QCD Amplitudes
• Unification of Residues and Grassmannian Dualities
• The super-correlator/super-amplitude duality: Part I
• Exacting N=4 Superconformal Symmetry
• Two-Loop Polygon Wilson Loops in N=4 SYM
• Symmetries of Tree-level Scattering Amplitudes in N=6 Superconformal Chern-Simons Theory
• Yangians, Grassmannians and T-duality
• The Yangian origin of the Grassmannian integral
• One-Loop Superconformal and Yangian Symmetries of Scattering Amplitudes in N=4 Super Yang-Mills
• All tree-level amplitudes in massless QCD
• Higgs-regularized three-loop four-gluon amplitude in N=4 SYM: exponentiation and Regge limits
• The Tree Formula for MHV Graviton Amplitudes
• New differential equations for on-shell loop integrals
• Scattering in Mass-Deformed N>=4 Chern-Simons Models
• Scattering amplitudes: the most perfect microscopic structures in the universe
• Proof of the MHV vertex expansion for all tree amplitudes in N=4 SYM theory
• Dual Conformal Properties of Six-Dimensional Maximal Super Yang-Mills Amplitudes
• Einstein-Yang-Mills from pure Yang-Mills amplitudes
• Solution to the Ward Identities for Superamplitudes
• Superconformal invariants for scattering amplitudes in N=4 SYM theory
• Massive amplitudes on the Coulomb branch of N=4 SYM
• R^4 counterterm and E7(7) symmetry in maximal supergravity
• Twistor-Strings, Grassmannians and Leading Singularities
• Scattering Amplitudes and BCFW Recursion in Twistor Space
• MHV Diagrams in Momentum Twistor Space
• Covariant Color-Kinematics Duality
• Local Integrand Representations of All Two-Loop Amplitudes in Planar SYM
• On-shell superamplitudes in N<4 SYM
• Yang-Baxter operators and scattering amplitudes in $\mathcal{N}=4$ super-Yang-Mills theory
• Simple loop integrals and amplitudes in N=4 SYM
• Spectral Parameters for Scattering Amplitudes in N=4 Super Yang-Mills Theory
• Yangian Symmetry of smooth Wilson Loops in N=4 super Yang-Mills Theory
• Helicity amplitudes for QCD with massive quarks
• On the Structure of Supersymmetric Sums in Multi-Loop Unitarity Cuts
• Constructing Amplitudes from Their Soft Limits
• Amplitudes, Form Factors and the Dilatation Operator in $\mathcal{N}=4$ SYM Theory
• An Introduction to On-shell Recursion Relations
• Tree-Level Amplitudes in N=8 Supergravity
• The Grassmannian and the Twistor String: Connecting All Trees in N=4 SYM
• A solution to the non-linear equations of D=10 super Yang-Mills theory
• Dual conformal symmetry of 1-loop NMHV amplitudes in N=4 SYM theory
• Unraveling L_{n,k}: Grassmannian Kinematics
• The Six-Point NMHV amplitude in Maximally Supersymmetric Yang-Mills Theory
• Dual conformal symmetry at loop level; massive regularization
• A First Course on Twistors, Integrability and Gluon Scattering Amplitudes
• Towards Field Theory Amplitudes From the Cohomology of Pure Spinor Superspace
• Composite Operators in the Twistor Formulation of $\mathcal{N}=4$ SYM Theory
• One-Loop Amplitudes in N=4 Super Yang-Mills and Anomalous Dual Conformal Symmetry
• Multi-Parton Scattering Amplitudes via On-Shell Methods
• Generating All Tree Amplitudes in N=4 SYM by Inverse Soft Limit
• N=4 Scattering Amplitudes and the Deformed Grassmannian
• Tree-Level Formalism
• Getting more flavour out of one-flavour QCD
• Grassmannians for scattering amplitudes in 4d $\mathcal{N}=4$ SYM and 3d ABJM
• All Tree-Level MHV Form Factors in $\mathcal{N}=4$ SYM from Twistor Space
• Monodromy--like Relations for Finite Loop Amplitudes
• Constructing $\mathcal{N}=4$ Coulomb Branch Superamplitudes
• U(1)-decoupling, KK and BCJ relations in $\mathcal{N}=4$ SYM
• Amplitudes at Weak Coupling as Polytopes in AdS_5
• A Direct Proof of BCFW Recursion for Twistor-Strings
• Exact Superconformal and Yangian Symmetry of Scattering Amplitudes
• Dual conformal invariance for form factors
• Review of AdS/CFT Integrability, Chapter V.2: Dual Superconformal Symmetry
• Yangian Invariants and Cluster Adjacency in N=4 Yang-Mills
• Positive helicity Einstein-Yang-Mills amplitudes from the Double Copy
• OPE for Super Loops
• Massive On-Shell Supersymmetric Scattering Amplitudes
• Form factor recursion relations at loop level
• What can we learn about QCD and collider physics from N=4 super Yang-Mills?
• Gluon Tree Amplitudes in Open Twistor String Theory
• From Six to Four and More: Massless and Massive Maximal Super Yang-Mills Amplitudes in 6d and 4d and their Hidden Symmetries
• An Etude on Recursion Relations and Triangulations
• Yangian Symmetry for the Action of Planar N=4 Super Yang-Mills and N=6 Super Chern-Simons Theories
• Inverse Soft Factors and Grassmannian Residues
• Null Wilson loops with a self-crossing and the Wilson loop/amplitude conjecture
• Pomerons and BCFW recursion relations for strings on D-branes
• A super MHV vertex expansion for N=4 SYM theory
• An Elliptic Yangian-Invariant, `Leading Singularity'
• MHV Diagrams from an All-Line Recursion Relation
• Comparing efficient computation methods for massless QCD tree amplitudes: Closed Analytic Formulae versus Berends-Giele Recursion
• Scattering Amplitudes and Toric Geometry
• Review of AdS/CFT Integrability, Chapter V.1: Scattering Amplitudes - a Brief Introduction
• Hidden Simplicity of Gauge Theory Amplitudes
• Hexagon POPE: effective particles and tree level resummation
• Conformal anomaly of super Wilson loop
• Compact QED Tree-Level Amplitudes From Dressed BCFW Recursion Relations
• Bootstrap and Amplitudes: A Hike in the Landscape of Quantum Field Theory
• All rational one-loop Einstein-Yang-Mills amplitudes at four points
• One-Loop Soft Theorems via Dual Superconformal Symmetry
• New relations for graviton-matter amplitudes
• All-multiplicity amplitudes with four massive quarks and identical-helicity gluons
• Note on Bonus Relations for N=8 Supergravity Tree Amplitudes
• General Split Helicity Gluon Tree Amplitudes in Open Twistor String Theory
• Manifest SO(N) invariance and S-matrices of three-dimensional N=2,4,8 SYM
• On the Classification of Residues of the Grassmannian
• Consistency Conditions on S-Matrix of Spin 1 Massless Particles
• Yangian Algebra and Correlation Functions in Planar Gauge Theories
• One-loop N=8 supergravity coefficients from N=4 super Yang-Mills
• Complete Equivalence Between Gluon Tree Amplitudes in Twistor String Theory and in Gauge Theory
• Non-planar BCFW Grassmannian Geometries
• Supersymmetric Massive Gravity
• ABJM Amplitudes in U-gauge and a Soft Theorem
• Holonomies of gauge fields in twistor space 1: bialgebra, supersymmetry, and gluon amplitudes
• Poles At Infinity in On-shell Diagrams
• From lightcone actions to maximally supersymmetric amplitudes
• Amplitudes from anomalous superconformal symmetry
• On All-loop Integrands of Scattering Amplitudes in Planar N=4 SYM
• Supersymmetric Yang-Mills and Supergravity Amplitudes at One Loop
• Twistor and Polytope Interpretations for Subleading Color One-Loop Amplitudes
• Permutation Relations of Yangian Invariants, Unitarity Cuts, and Scattering Amplitudes
• Generating MHV super-vertices in light-cone gauge
• Nonplanar On-shell Diagrams and Leading Singularities of Scattering Amplitudes
• Minimally helicity violating, maximally simple scalar amplitudes in N=4 SYM
• Yangian symmetry of light-like Wilson loops
• Locally Finite Observables in sYM
• All one-loop NMHV gluon amplitudes in N=1 SYM
• Positivity, Grassmannian Geometry and Simplex-like Structures of Scattering Amplitudes
• Grassmannian Integrals in Minkowski Signature, Amplitudes, and Integrability
• Weak Separation, Positivity and Extremal Yangian Invariants
• Tree-level Split Helicity Amplitudes in Ambitwistor Space
• New N=4 SYM Path Integral
• Supersums for all supersymmetric amplitudes
• A connection between $\mathcal{R}$-invariants and Yang-Baxter $R$-operators in $\mathcal{N}=4$ super-Yang-Mills theory
• Bilocal phase operators in beta-deformed super Yang-Mills
• A Celestial Description of Planar Super-Yang-Mills Theory
• Simplex-like Structures of Maximally Supersymmetric Scattering Amplitudes
• Cyclicity of All Anti-NMHV and N${}^2$MHV Tree Amplitudes in N=4 SYM