A note on dual superconformal symmetry of the N=4 super Yang-Mills S-matrix

Abstract

We present a supersymmetric recursion relation for tree-level scattering amplitudes in N=4 super Yang-Mills. Using this recursion relation, we prove that the tree-level S-matrix of the maximally supersymmetric theory is covariant under dual superconformal transformations. We further analyse the consequences that the transformation properties of the trees under this symmetry have on those of the loops. In particular, we show that the coefficients of the expansion of generic one-loop amplitudes in a basis of pseudo-conformally invariant scalar box functions transform covariantly under dual superconformal symmetry, and in exactly the same way as the corresponding tree-level amplitudes.

30 pages, 4 figures; v2: Section 2.1, added proof of covariance under dual conformal inversions of 3-point anti-MHV amplitude; Section 5, conjecture on dual conformal covariance of one-loop amplitude coefficients converted to a proof; typos corrected; v3: changes in Section 2.2, one reference added

References in corpus (8)

• 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
• Hexagon Wilson loop = six-gluon MHV amplitude
• The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory
• The hexagon Wilson loop and the BDS ansatz for the six-gluon amplitude
• Generating Tree Amplitudes in N=4 SYM and N=8 SG
• Two-Loop Iteration of Five-Point N=4 Super-Yang-Mills Amplitudes

Cited by in corpus (62)

• Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory
• Loop Corrections to Soft Theorems in Gauge Theories and Gravity
• BFKL Pomeron, Reggeized gluons and Bern-Dixon-Smirnov amplitudes
• All tree-level amplitudes in N=4 SYM
• The Complete Four-Loop Four-Point Amplitude in N=4 Super-Yang-Mills Theory
• Exacting N=4 Superconformal Symmetry
• One-Loop Superconformal and Yangian Symmetries of Scattering Amplitudes in N=4 Super Yang-Mills
• The Yangian origin of the Grassmannian integral
• 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
• Spinor Helicity and Dual Conformal Symmetry in Ten Dimensions
• New differential equations for on-shell loop integrals
• Recursion Relations for AdS/CFT Correlators
• BCFW for Witten Diagrams
• 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
• Recursion Relations, Generating Functions, and Unitarity Sums in N=4 SYM Theory
• MHV Diagrams in Momentum Twistor Space
• Conformal Anomaly for Amplitudes in N=6 Superconformal Chern-Simons Theory
• Simple loop integrals and amplitudes in N=4 SYM
• Eliminating spurious poles from gauge-theoretic amplitudes
• On AdS_4 x CP^3 T-duality
• Tree-Level Amplitudes in N=8 Supergravity
• 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
• One-Loop Amplitudes in N=4 Super Yang-Mills and Anomalous Dual Conformal Symmetry
• T-Duality, Dual Conformal Symmetry and Integrability for Strings on AdS_5 x S^5
• Bonus Yangian Symmetry for the Planar S-Matrix of N=4 Super Yang-Mills
• Proof of the Dual Conformal Anomaly of One-Loop Amplitudes in N=4 SYM
• Amplitudes at Infinity
• 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
• Soft theorems in maximally supersymmetric theories
• Celestial Superamplitudes
• On the ABJM four-point amplitude at three loops and BDS exponentiation
• Form factor recursion relations at loop level
• What can we learn about QCD and collider physics from N=4 super Yang-Mills?
• A super MHV vertex expansion for N=4 SYM theory
• Null Polygonal Wilson Loops in Full N=4 Superspace
• Cross-Order Integral Relations from Maximal Cuts
• Soft Theorems from Effective Field Theory
• The Coulomb-branch S-matrix from massless amplitudes
• Double-Soft Limits of Gluons and Gravitons
• On three-point functions in ABJM and the latitude Wilson loop
• One-loop N=8 supergravity coefficients from N=4 super Yang-Mills
• Massive On-shell Recursion Relations for n-point Amplitudes
• Yangian in the Twistor String
• $\mathcal{N}=7$ On-Shell Diagrams and Supergravity Amplitudes in Momentum Twistor Space
• Holonomies of gauge fields in twistor space 1: bialgebra, supersymmetry, and gluon amplitudes
• 6d Dual Conformal Symmetry and Minimal Volumes in AdS
• Supersymmetric Yang-Mills and Supergravity Amplitudes at One Loop
• Locally Finite Observables in sYM
• Perturbative Methods for Superconformal Quantum Field Theories in String - Gauge Theory Dualities
• Yangian Symmetry in Five Dimensions
• New N=4 SYM Path Integral
• Orientations of BCFW Charts on the Grassmannian
• Symplectic Grassmannians, dual conformal symmetry and 4-point amplitudes in 6D
• BCFW like recursion for Deformed Associahedron