One-Loop Amplitudes in N=4 Super Yang-Mills and Anomalous Dual Conformal Symmetry

Abstract

We discuss what predictions can be made for one-loop superamplitudes in maximally supersymmetric Yang-Mills theory by using anomalous dual conformal symmetry. We show that the anomaly coefficient is a specific combination of two-mass hard and one-mass supercoefficients which appears in the supersymmetric on-shell recursion relations and equals the corresponding tree-level superamplitude. We discuss further novel relations among supercoefficients imposed by the remaining non-anomalous part of the symmetry. In particular, we find that all one-loop supercoefficients, except the four-mass box coefficients, can be expressed as linear combinations of three-mass box coefficients and a particular symmetric combination of two-mass hard coefficients. We check that our equations are explicitly satisfied in the case of one-loop n-point MHV and NMHV amplitudes. As a bonus, we prove the covariance of the NMHV superamplitudes at an arbitrary number of points, extending previous results at n <= 9.

30 pages, 3 figures

References in corpus (40)

• One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits
• Fusing Gauge Theory Tree Amplitudes Into Loop Amplitudes
• New Recursion Relations for Tree Amplitudes of Gluons
• Gluon scattering amplitudes at strong coupling
• Iteration of Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory at Three Loops and Beyond
• Dual superconformal symmetry of scattering amplitudes in N=4 super-Yang-Mills theory
• Conformal properties of four-gluon planar amplitudes and Wilson loops
• What is the Simplest Quantum Field Theory?
• MHV Amplitudes in N=4 Super Yang-Mills and Wilson Loops
• Magic identities for conformal four-point integrals
• The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory
• Conformal Ward identities for Wilson loops and a test of the duality with gluon amplitudes
• On planar gluon amplitudes/Wilson loops duality
• Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory
• Hexagon Wilson loop = six-gluon MHV amplitude
• Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory
• The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory
• Fermionic T-Duality, Dual Superconformal Symmetry, and the Amplitude/Wilson Loop Connection
• Maximally Supersymmetric Planar Yang-Mills Amplitudes at Five Loops
• One-Loop Gauge Theory Amplitudes in N=4 Super Yang-Mills from MHV Vertices
• Dual Superconformal Symmetry from AdS5 x S5 Superstring Integrability
• A note on dual superconformal symmetry of the N=4 super Yang-Mills S-matrix
• Tree Amplitudes in Gauge Theory as Scalar MHV Diagrams
• The hexagon Wilson loop and the BDS ansatz for the six-gluon amplitude
• Generating Tree Amplitudes in N=4 SYM and N=8 SG
• All tree-level amplitudes in N=4 SYM
• Two-Loop Iteration of Five-Point N=4 Super-Yang-Mills Amplitudes
• Generalized unitarity for N=4 super-amplitudes
• Exacting N=4 Superconformal Symmetry
• All Next-to-Maximally-Helicity-Violating One-Loop Gluon Amplitudes in N=4 Super-Yang-Mills Theory
• Four-Loop Cusp Anomalous Dimension From Obstructions
• Two-Loop Polygon Wilson Loops in N=4 SYM
• Dissolving N=4 loop amplitudes into QCD tree amplitudes
• Proof of the MHV vertex expansion for all tree amplitudes in N=4 SYM theory
• Recursion Relations, Generating Functions, and Unitarity Sums in N=4 SYM Theory
• Iterative Structure Within The Five-Particle Two-Loop Amplitude
• Three-Loop Leading Singularities and BDS Ansatz for Five Particles
• On the Structure of Supersymmetric Sums in Multi-Loop Unitarity Cuts
• Dual conformal symmetry of 1-loop NMHV amplitudes in N=4 SYM theory
• Higher point MHV amplitudes in N=4 Supersymmetric Yang-Mills Theory

Cited by in corpus (33)

• The All-Loop Integrand For Scattering Amplitudes in Planar N=4 SYM
• Dual Superconformal Invariance, Momentum Twistors and Grassmannians
• Scattering into the fifth dimension of N=4 super Yang-Mills
• One-Loop Superconformal and Yangian Symmetries of Scattering Amplitudes in N=4 Super Yang-Mills
• Higgs-regularized three-loop four-gluon amplitude in N=4 SYM: exponentiation and Regge limits
• Symmetries and analytic properties of scattering amplitudes in N=4 SYM theory
• Dual Conformal Properties of Six-Dimensional Maximal Super Yang-Mills Amplitudes
• Solution to the Ward Identities for Superamplitudes
• Massive amplitudes on the Coulomb branch of N=4 SYM
• Superconformal invariants for scattering amplitudes in N=4 SYM theory
• On-shell superamplitudes in N<4 SYM
• Dualities for Loop Amplitudes of N=6 Chern-Simons Matter Theory
• On Yangian Symmetry in Planar N=4 SYM
• Dual conformal symmetry of 1-loop NMHV amplitudes in N=4 SYM theory
• MHV diagrams in twistor space and the twistor action
• A note on amplitudes in N=6 superconformal Chern-Simons theory
• Proof of the Dual Conformal Anomaly of One-Loop Amplitudes in N=4 SYM
• Grassmannians for scattering amplitudes in 4d $\mathcal{N}=4$ SYM and 3d ABJM
• From Polygon Wilson Loops to Spin Chains and Back
• Dual conformal invariance for form factors
• OPE for Super Loops
• Perturbative correlation functions of null Wilson loops and local operators
• The two-loop MHV amplitudes in N=4 supersymmetric Yang-Mills theory
• Hidden Simplicity of Gauge Theory Amplitudes
• Global Poles of the Two-Loop Six-Point N=4 SYM integrand
• The Coulomb-branch S-matrix from massless amplitudes
• Scattering amplitudes at strong coupling for 4K gluons
• Holonomies of gauge fields in twistor space 1: bialgebra, supersymmetry, and gluon amplitudes
• One-loop N = 4 super Yang-Mills scattering amplitudes in d dimensions, relation to open strings and polygonal Wilson loops
• Dual conformal constraints and infrared equations from global residue theorems in N=4 SYM theory
• Locally Finite Observables in sYM
• Holonomies of gauge fields in twistor space 4: functional MHV rules and one-loop amplitudes
• Perturbative Methods for Superconformal Quantum Field Theories in String - Gauge Theory Dualities