Superconformal symmetry and two-loop amplitudes in planar N=4 super Yang-Mills

Abstract

Scattering amplitudes in superconformal field theories do not enjoy this symmetry, because the definition of asymptotic states involve a notion of infinity. Concentrating on planar $\mathcal{N}=4$ Yang-Mills, we consider a generalization of scattering amplitudes which depends on twice as many Grassmann variables. We conjecture that it restores at least half of the superconformal symmetries, and all of the dual superconformal symmetries. The object arises naturally as the dual of a null polygonal Wilson loop in an $(x,\theta ,\bar{\theta })$ superspace. We support the conjecture by using it to obtain the total differential of all $n$-point two-loop MHV amplitudes, and showing that the result passes consistency checks. Potential all-loop constraints are also discussed.

25 pages, 2 figures and 1 notebook

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Cited by in corpus (117)

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• Motivic Amplitudes and Cluster Coordinates
• Analytic result for the two-loop six-point NMHV amplitude in N=4 super Yang-Mills theory
• A Symbol of Uniqueness: The Cluster Bootstrap for the 3-Loop MHV Heptagon
• Heptagons from the Steinmann Cluster Bootstrap
• Jumpstarting the all-loop S-matrix of planar N=4 super Yang-Mills
• Hexagon functions and the three-loop remainder function
• Space-time S-matrix and Flux tube S-matrix II. Extracting and Matching Data
• The four-loop remainder function and multi-Regge behavior at NNLLA in planar N=4 super-Yang-Mills theory
• Single-valued harmonic polylogarithms and the multi-Regge limit
• Six-Gluon Amplitudes in Planar $\mathcal{N}=4$ Super-Yang-Mills Theory at Six and Seven Loops
• Analytic two-loop form factors in N=4 SYM
• Iterative structure of finite loop integrals
• A (Bounded) Bestiary of Feynman Integral Calabi-Yau Geometries
• Cluster adjacency properties of scattering amplitudes
• The Cosmic Galois Group and Extended Steinmann Relations for Planar $\mathcal{N}=4$ SYM Amplitudes
• Space-time S-matrix and Flux-tube S-matrix IV. Gluons and Fusion
• Multi-Regge kinematics and the moduli space of Riemann spheres with marked points
• Multiple polylogarithms with algebraic arguments and the two-loop EW-QCD Drell-Yan master integrals
• OPE for all Helicity Amplitudes
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• Embedding Feynman Integral (Calabi-Yau) Geometries in Weighted Projective Space
• A Cluster Bootstrap for Two-Loop MHV Amplitudes
• A Three-Point Form Factor Through Five Loops
• Cluster adjacency beyond MHV
• Conformal Anomaly for Amplitudes in N=6 Superconformal Chern-Simons Theory
• Sequential Discontinuities of Feynman Integrals and the Monodromy Group
• Yangian Symmetry of smooth Wilson Loops in N=4 super Yang-Mills Theory
• The two-loop five-particle amplitude in $\mathcal{N}=8$ supergravity
• Hexagon Wilson Loop OPE and Harmonic Polylogarithms
• How tropical are seven- and eight-particle amplitudes?
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• Implications of the Landau Equations for Iterated Integrals
• Landau Singularities from the Amplituhedron
• Landau Singularities and Symbology: One- and Two-loop MHV Amplitudes in SYM Theory
• Bootstrapping a Stress-Tensor Form Factor through Eight Loops
• An analytic result for the two-loop seven-point MHV amplitude in N=4 SYM
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• Two-loop Octagons, Algebraic Letters and $\bar{Q}$ Equations
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• From dlogs to dilogs; the super Yang-Mills MHV amplitude revisited
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• The Differential of All Two-Loop MHV Amplitudes in N=4 Yang-Mills Theory
• The elliptic double box and symbology beyond polylogarithms
• Hexagon OPE Resummation and Multi-Regge Kinematics
• Boundaries of Amplituhedra and NMHV Symbol Alphabets at Two Loops
• Prescriptive Unitarity for Non-Planar Six-Particle Amplitudes at Two Loops
• Descent equations for superamplitudes
• Notes on cluster algebras and some all-loop Feynman integrals
• The symbol and alphabet of two-loop NMHV amplitudes from $\bar{Q}$ equations
• Symbol Alphabets from Plabic Graphs
• Tropical fans, scattering equations and amplitudes
• The Sklyanin Bracket and Cluster Adjacency at All Multiplicity
• Amplitudes from superconformal Ward identities
• All-Helicity Symbol Alphabets from Unwound Amplituhedra
• Symbol Alphabets from Tensor Diagrams
• Three-loop octagons and n-gons in maximally supersymmetric Yang-Mills theory
• Multichannel Conformal Blocks for Polygon Wilson Loops
• Constraints on Sequential Discontinuities from the Geometry of On-shell Spaces
• Yangian Invariants and Cluster Adjacency in N=4 Yang-Mills
• Cluster Algebras and the Subalgebra Constructibility of the Seven-Particle Remainder Function
• All Two-Loop MHV Amplitudes in Multi-Regge Kinematics From Applied Symbology
• Bootstrapping elliptic Feynman integrals using Schubert analysis
• Feynman Integrals and Scattering Amplitudes from Wilson Loops
• Towards single-valued polylogarithms in two variables for the seven-point remainder function in multi-Regge-kinematics
• The Wilson-loop $d\log$ representation for Feynman integrals
• Bootstrapping a Two-Loop Four-Point Form Factor
• Heptagon Amplitude in the Multi-Regge Regime
• The Two-Loop Remainder Function for Eight and Nine Particles
• Null Polygonal Wilson Loops in Full N=4 Superspace
• The Two-Loop Symbol of all Multi-Regge Regions
• Cluster Polylogarithms for Scattering Amplitudes
• Hedgehog Bases for A_n Cluster Polylogarithms and An Application to Six-Point Amplitudes
• The Three-loop MHV Octagon from $\bar{Q}$ equations
• Rooting Out Letters: Octagonal Symbol Alphabets and Algebraic Number Theory
• Smooth Wilson Loops in N=4 Non-Chiral Superspace
• An Infinite Family of Elliptic Ladder Integrals
• One-Loop Soft Theorems via Dual Superconformal Symmetry
• Comments on all-loop constraints for scattering amplitudes and Feynman integrals
• The SAGEX Review on Scattering Amplitudes, Chapter 15: The Multi-Regge Limit
• On the Geometry of Null Polygons in Full N=4 Superspace
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• The two-loop eight-point amplitude in ABJM theory
• The SAGEX Review on Scattering Amplitudes, Chapter 5: Analytic Bootstraps for Scattering Amplitudes and Beyond
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• Conformally Regulated Direct Integration of the Two-Loop Heptagon Remainder
• Hexagon remainder function in the limit of self-crossing up to three loops
• An Origin Story for Amplitudes
• Yangian Symmetry in N=4 super Yang-Mills
• Amplitudes from anomalous superconformal symmetry
• Systematics of the Multi-Regge Three-Loop Symbol
• The dimension-shift conjecture for one-loop amplitudes
• A nice two-loop next-to-next-to-MHV amplitude in $\mathcal{N}=4$ super-Yang-Mills
• Antipodal Symmetry of Two-Loop MHV Amplitudes
• A Novel Algorithm for Nested Summation and Hypergeometric Expansions
• Supersymmetric Wilson Loops via Integral Forms
• 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
• Permutation Relations of Yangian Invariants, Unitarity Cuts, and Scattering Amplitudes
• The Steinmann Cluster Bootstrap for N=4 Super Yang-Mills Amplitudes
• Wilson loops in N=6 superspace for ABJM theory
• The Multi-Regge Limit from the Wilson Loop OPE
• Nonplanar On-shell Diagrams and Leading Singularities of Scattering Amplitudes
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• Twistors, Harmonics and Holomorphic Chern-Simons
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• Higher-Point Correlators in N=4 SYM: Ten-Dimensional Null Polygons
• Twistor Parametrization of Locally BPS Super-Wilson Loops
• Cluster Functions and Scattering Amplitudes for Six and Seven Points