One-Loop Superconformal and Yangian Symmetries of Scattering Amplitudes in N=4 Super Yang-Mills

Abstract

Recently it has been argued that tree-level scattering amplitudes in N=4 Yang-Mills theory are uniquely determined by a careful study of their superconformal and Yangian symmetries. However, at one-loop order these symmetries are known to become anomalous due to infrared divergences. We compute these one-loop anomalies for amplitudes defined through dimensional regularisation by studying the tree-level symmetry transformations of the unitarity branch cuts, keeping track of the crucial collinear terms arising from the holomorphic anomaly. We extract the superconformal anomalies and show that they may be cancelled through a universal one-loop deformation of the tree-level symmetry generators which involves only tree-level data. Specialising to the planar theory we also obtain the analogous deformation for the level-one Yangian generator of momentum. Explicit checks of our one-loop deformation are performed for MHV and the 6-point NMHV amplitudes.

64 pages, v2: typos and minor corrections in (6.14) and (6.17), to appear in JHEP

References in corpus (25)

• Gluon scattering amplitudes at strong coupling
• Conformal collider physics: Energy and charge correlations
• Conformal properties of four-gluon planar amplitudes and Wilson loops
• MHV Amplitudes in N=4 Super Yang-Mills and Wilson Loops
• The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory
• Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory
• Hexagon Wilson loop = six-gluon MHV amplitude
• The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory
• Maximally Supersymmetric Planar Yang-Mills Amplitudes at Five Loops
• Dual Superconformal Symmetry from AdS5 x S5 Superstring Integrability
• A note on dual superconformal symmetry of the N=4 super Yang-Mills S-matrix
• Scattering Amplitudes, Wilson Loops and the String/Gauge Theory Correspondence
• Generating Tree Amplitudes in N=4 SYM and N=8 SG
• All tree-level amplitudes in N=4 SYM
• Exacting N=4 Superconformal Symmetry
• Higgs-regularized three-loop four-gluon amplitude in N=4 SYM: exponentiation and Regge limits
• The Classical r-matrix of AdS/CFT and its Lie Bialgebra Structure
• Recursion Relations, Generating Functions, and Unitarity Sums in N=4 SYM Theory
• Holomorphic Anomaly Of Unitarity Cuts And One-Loop Gauge Theory Amplitudes
• 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
• Symmetries of the N=4 SYM S-matrix
• Proof of the Dual Conformal Anomaly of One-Loop Amplitudes in N=4 SYM
• Yangian Symmetry of Long-Range gl(N) Integrable Spin Chains
• Infrared Safe Observables in $\mathcal{N}=4$ Super Yang-Mills Theory

Cited by in corpus (17)

• The All-Loop Integrand For Scattering Amplitudes in Planar N=4 SYM
• The Complete Four-Loop Four-Point Amplitude in N=4 Super-Yang-Mills Theory
• The Yangian origin of the Grassmannian integral
• On form factors in N=4 sym
• New differential equations for on-shell loop integrals
• Dual Conformal Properties of Six-Dimensional Maximal Super Yang-Mills Amplitudes
• Lectures on Yangian Symmetry
• Conformal Anomaly for Amplitudes in N=6 Superconformal Chern-Simons Theory
• One Loop Amplitudes In ABJM
• On AdS_4 x CP^3 T-duality
• The Six-Point NMHV amplitude in Maximally Supersymmetric Yang-Mills Theory
• Bonus Yangian Symmetry for the Planar S-Matrix of N=4 Super Yang-Mills
• Introduction to Integrability and One-point Functions in $\mathcal{N}=4$ SYM and its Defect Cousin
• Heat kernel expansion and induced action for the matrix model Dirac operator
• Perturbative Methods for Superconformal Quantum Field Theories in String - Gauge Theory Dualities
• Commuting Conformal and Dual Conformal Symmetries in the Regge limit
• Scattering Amplitudes in Gauge Theories