Iterative Structure Within The Five-Particle Two-Loop Amplitude

Abstract

We find an unexpected iterative structure within the two-loop five-gluon amplitude in N = 4 supersymmetric Yang-Mills theory. Specifically, we show that a subset of diagrams contributing to the full amplitude, including a two-loop pentagon-box integral with nontrivial dependence on five kinematical variables, satisfies an iterative relation in terms of one-loop scalar box diagrams. The implications of this result for the possible iterative structure of the full two-loop amplitude are discussed.

22 pages, revtex4

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• Conformal Ward identities for Wilson loops and a test of the duality with gluon amplitudes
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• Maximally Supersymmetric Planar Yang-Mills Amplitudes at Five Loops
• Simplifying Multiloop Integrands and Ultraviolet Divergences of Gauge Theory and Gravity Amplitudes
• The Two-Loop Hexagon Wilson Loop in N = 4 SYM
• Scattering Amplitudes, Wilson Loops and the String/Gauge Theory Correspondence
• The hexagon Wilson loop and the BDS ansatz for the six-gluon amplitude
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• An Analytic Result for the Two-Loop Hexagon Wilson Loop in N = 4 SYM
• Analytic form of the two-loop planar five-gluon all-plus-helicity amplitude in QCD
• Extension of HPL to complex arguments
• The super-correlator/super-amplitude duality: Part I
• The Complete Four-Loop Four-Point Amplitude in N=4 Super-Yang-Mills Theory
• Two-Loop Iteration of Five-Point N=4 Super-Yang-Mills Amplitudes
• Sharpening The Leading Singularity
• Four-Loop Cusp Anomalous Dimension From Obstructions
• Two-Loop Polygon Wilson Loops in N=4 SYM
• Analytic result for a two-loop five-particle amplitude
• More on the duality correlators/amplitudes
• The super-correlator/super-amplitude duality: Part II
• The Soft-Collinear Bootstrap: N=4 Yang-Mills Amplitudes at Six and Seven Loops
• Leading Singularities of the Two-Loop Six-Particle MHV Amplitude
• More loops and legs in Higgs-regulated N=4 SYM amplitudes
• On MHV Form Factors in Superspace for $\mathcal{N}=4$ SYM Theory
• The one-loop six-dimensional hexagon integral and its relation to MHV amplitudes in N=4 SYM
• Iterated amplitudes in the high-energy limit
• Three-Loop Leading Singularities and BDS Ansatz for Five Particles
• On the Structure of Supersymmetric Sums in Multi-Loop Unitarity Cuts
• New Dual Conformally Invariant Off-Shell Integrals
• The Six-Point NMHV amplitude in Maximally Supersymmetric Yang-Mills Theory
• Four-Loop Collinear Anomalous Dimension in N = 4 Yang-Mills Theory
• Duality between Wilson loops and gluon amplitudes
• Analyticity for Multi-Regge Limits of the Bern-Dixon-Smirnov Amplitudes
• One-Loop Amplitudes in N=4 Super Yang-Mills and Anomalous Dual Conformal Symmetry
• Simplicity of Polygon Wilson Loops in N=4 SYM
• Scattering amplitudes in strongly coupled N=4 SYM from semiclassical strings in AdS
• Review of AdS/CFT Integrability, Chapter V.2: Dual Superconformal Symmetry
• The Imaginary Part of the N = 4 Super-Yang-Mills Two-Loop Six-Point MHV Amplitude in Multi-Regge Kinematics
• Cross-Order Integral Relations from Maximal Cuts
• The two-loop MHV amplitudes in N=4 supersymmetric Yang-Mills theory
• Hidden Simplicity of Gauge Theory Amplitudes
• On the two-loop hexagon Wilson loop remainder function in N=4 SYM
• MHV amplitudes in N=2 SQCD and in N=4 SYM at one loop
• Construction of Infrared Finite Observables in N=4 Super Yang-Mills Theory
• Higher point MHV amplitudes in N=4 Supersymmetric Yang-Mills Theory
• Infrared Safe Observables in $\mathcal{N}=4$ Super Yang-Mills Theory
• Maximal transcendental weight contribution of scattering amplitudes
• Loop lessons from Wilson loops in N=4 supersymmetric Yang-Mills theory
• 6d Dual Conformal Symmetry and Minimal Volumes in AdS
• A Note on Loop Amplitudes in QED
• Asymptotic AdS String Solutions for Null Polygonal Wilson Loops in R^{1,2}
• Supersums for all supersymmetric amplitudes
• On perturbative field theory and twistor string theory
• MHV amplitudes, Wilson loops and the BDS ansatz in the superconformal N=2 QCD