Descent equations for superamplitudes

Abstract

At loop level in planar N=4 super Yang-Mills, the dual superconformal symmetry of tree amplitudes is lost. This is true even if one uses a supersymmetry preserving regulator, and even for finite quantities that remain dual conformally invariant. We examine this breaking from the dual point of view of the super Wilson Loop, tracing it to the difference between supersymmetries of the self-dual and of the full theories. We show that the anomaly is controlled by a descent equation that determines the derivative of an L-loop amplitude in terms of a single non-trivial integral of an (L-1)-loop amplitude. We propose that this equation can be used recursively to construct multi-loop amplitudes in a way that makes their transcendentality manifest.

27 pages, 4 figures

References in corpus (9)

• Classical Polylogarithms for Amplitudes and Wilson Loops
• Conformal properties of four-gluon planar amplitudes and Wilson loops
• MHV Amplitudes in N=4 Super Yang-Mills and Wilson Loops
• The Complete Planar S-matrix of N=4 SYM as a Wilson Loop in Twistor Space
• Exacting N=4 Superconformal Symmetry
• The Yangian origin of the Grassmannian integral
• MHV Diagrams in Momentum Twistor Space
• Symmetries of the N=4 SYM S-matrix
• Holomorphic Linking, Loop Equations and Scattering Amplitudes in Twistor Space

Cited by in corpus (24)

• Motivic Amplitudes and Cluster Coordinates
• Bootstrapping an NMHV amplitude through three loops
• A Symbol of Uniqueness: The Cluster Bootstrap for the 3-Loop MHV Heptagon
• Cluster adjacency beyond MHV
• Conformal Anomaly for Amplitudes in N=6 Superconformal Chern-Simons Theory
• On NMHV form factors in N=4 SYM theory from generalized unitarity
• A "Twistor String" Inspired Formula For Tree-Level Scattering Amplitudes in N=8 SUGRA
• Bethe Ansatz for Yangian Invariants: Towards Super Yang-Mills Scattering Amplitudes
• From the Holomorphic Wilson Loop to `d log' Loop-Integrands of Super-Yang-Mills Amplitudes
• Conformal anomaly of generalized form factors and finite loop integrals
• From Polygon Wilson Loops to Spin Chains and Back
• All Two-Loop MHV Amplitudes in Multi-Regge Kinematics From Applied Symbology
• Bootstrapping six-gluon scattering in planar $\mathcal{N}=4$ super-Yang-Mills theory
• Null Polygonal Wilson Loops in Full N=4 Superspace
• Nonperturbative enhancement of superloop at strong coupling
• Towards NMHV amplitudes at strong coupling
• Dual conformal symmetry on the light-cone
• On the Geometry of Null Polygons in Full N=4 Superspace
• The four-loop six-gluon NMHV ratio function
• Twistor fishnets
• Descent equation for superloop and cyclicity of OPE
• Twistors, Harmonics and Holomorphic Chern-Simons
• Perturbative Methods for Superconformal Quantum Field Theories in String - Gauge Theory Dualities
• Twistor Parametrization of Locally BPS Super-Wilson Loops