Superconformal invariants for scattering amplitudes in N=4 SYM theory

Abstract

Recent studies of scattering amplitudes in planar N=4 SYM theory revealed the existence of a hidden dual superconformal symmetry. Together with the conventional superconformal symmetry it gives rise to powerful restrictions on the planar scattering amplitudes to all loops. We study the general form of the invariants of both symmetries. We first construct an integral representation for the most general dual superconformal invariants and show that it allows a considerable freedom in the choice of the integration measure. We then perform a half-Fourier transform to twistor space, where conventional conformal symmetry is realized locally, derive the resulting conformal Ward identity for the integration measure and show that it admits a unique solution. Thus, the combination of dual and conventional superconformal symmetries, together with invariance under helicity rescalings, completely fixes the form of the invariants. The expressions obtained generalize the known tree and one-loop superconformal invariants and coincide with the recently proposed coefficients of the leading singularities of the scattering amplitudes as contour integrals over Grassmannians.

44 pages; the discussion of dual superconformal invariants in Sect. 3 extended; new appendix added; references added

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Cited by in corpus (55)

• The All-Loop Integrand For Scattering Amplitudes in Planar N=4 SYM
• Towards a Basis for Planar Two-Loop Integrals
• Analytic result for the two-loop six-point NMHV amplitude in N=4 super Yang-Mills theory
• Superconformal symmetry and two-loop amplitudes in planar N=4 super Yang-Mills
• Notes on the scattering amplitude / Wilson loop duality
• Jumpstarting the all-loop S-matrix of planar N=4 super Yang-Mills
• The super-correlator/super-amplitude duality: Part I
• Basics of Generalized Unitarity
• Tree-level Recursion Relation and Dual Superconformal Symmetry of the ABJM Theory
• Symmetries of Tree-level Scattering Amplitudes in N=6 Superconformal Chern-Simons Theory
• The Yangian origin of the Grassmannian integral
• New differential equations for on-shell loop integrals
• OPE for all Helicity Amplitudes
• Dual Conformal Properties of Six-Dimensional Maximal Super Yang-Mills Amplitudes
• Amplitudes of 3D and 6D Maximal Superconformal Theories in Supertwistor Space
• OPE for all Helicity Amplitudes II. Form Factors and Data Analysis
• 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
• Towards the Amplituhedron Volume
• The Grassmannian and the Twistor String: Connecting All Trees in N=4 SYM
• Two-loop Octagons, Algebraic Letters and $\bar{Q}$ Equations
• The Six-Point NMHV amplitude in Maximally Supersymmetric Yang-Mills Theory
• Bethe Ansatz for Yangian Invariants: Towards Super Yang-Mills Scattering Amplitudes
• MHV diagrams in twistor space and the twistor action
• Fixing the Quantum Three-Point Function
• The symbol and alphabet of two-loop NMHV amplitudes from $\bar{Q}$ equations
• Exact Superconformal and Yangian Symmetry of Scattering Amplitudes
• Dual conformal invariance for form factors
• Non-Chiral S-Matrix of N=4 Super Yang-Mills
• Soft theorems in maximally supersymmetric theories
• Feynman Integrals and Scattering Amplitudes from Wilson Loops
• The Wilson-loop $d\log$ representation for Feynman integrals
• Inverse Soft Factors and Grassmannian Residues
• Null Polygonal Wilson Loops in Full N=4 Superspace
• Hidden Simplicity of Gauge Theory Amplitudes
• The Three-loop MHV Octagon from $\bar{Q}$ equations
• Global Poles of the Two-Loop Six-Point N=4 SYM integrand
• On the Classification of Residues of the Grassmannian
• Multi-Particle Amplitudes from the Four-Point Correlator in Planar N=4 SYM
• Correlators with $s{\ell }_2$ Yangian symmetry
• Tree-level scattering amplitudes from the amplituhedron
• One-loop N = 4 super Yang-Mills scattering amplitudes in d dimensions, relation to open strings and polygonal Wilson loops
• Yangian Symmetry in N=4 super Yang-Mills
• On All-loop Integrands of Scattering Amplitudes in Planar N=4 SYM
• Twistor and Polytope Interpretations for Subleading Color One-Loop Amplitudes
• One-Loop N = 4 Super Yang-Mills Scattering Amplitudes to All Orders in the Dimensional Regularization Parameter
• Yangian symmetry of light-like Wilson loops
• Locally Finite Observables in sYM
• Differential equations for multi-loop integrals and two-dimensional kinematics
• Perturbative Methods for Superconformal Quantum Field Theories in String - Gauge Theory Dualities
• Commuting Conformal and Dual Conformal Symmetries in the Regge limit
• Higher Codimension Singularities Constructing Yang-Mills Tree Amplitudes
• A connection between $\mathcal{R}$-invariants and Yang-Baxter $R$-operators in $\mathcal{N}=4$ super-Yang-Mills theory
• A Celestial Description of Planar Super-Yang-Mills Theory