Dual conformal symmetry at loop level; massive regularization

Abstract

Dual conformal symmetry has had a huge impact on our understanding of planar scattering amplitudes in N=4 super Yang-Mills. At tree level, it combines with the original conformal symmetry generators to a Yangian algebra, a hallmark of integrability, and helps in determining the tree-level amplitudes. The latter are now known in closed form. At loop level, it determines the functional form of the four- and five-point scattering amplitudes to all orders in the coupling constant, and gives restrictions at six points and beyond. The symmetry is best understood at loop level in terms of a novel AdS-inspired infrared regularization which makes the symmetry exact, despite the infrared divergences. This has important consequences for the basis of loop integrals in this theory. Recently, a number of selective reviews have appeared which discuss dual conformal symmetry, mostly at tree level. Here, we give an up-to-date account of dual conformal symmetry, focussing on its status at loop level.

18 pages, 5 figures, Invited review for a special issue of Journal of Physics A devoted to "Scattering Amplitudes in Gauge Theories", R. Roiban(ed), M. Spradlin(ed), A. Volovich(ed)

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Cited by in corpus (30)

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• Gravitational Effective Field Theory Islands, Low-Spin Dominance, and the Four-Graviton Amplitude
• Basics of Generalized Unitarity
• Generic multiloop methods and application to N=4 super-Yang-Mills
• Diagrammatic Hopf algebra of cut Feynman integrals: the one-loop case
• Scattering amplitudes: the most perfect microscopic structures in the universe
• Massive amplitudes on the Coulomb branch of N=4 SYM
• D = 5 maximally supersymmetric Yang-Mills theory diverges at six loops
• Yangian Symmetry for Bi-Scalar Loop Amplitudes
• The Five-Loop Four-Point Amplitude of N=4 super-Yang-Mills Theory
• Integrand Reduction for Two-Loop Scattering Amplitudes through Multivariate Polynomial Division
• The one-loop six-dimensional hexagon integral and its relation to MHV amplitudes in N=4 SYM
• Three Point Energy Correlators in the Collinear Limit: Symmetries, Dualities and Analytic Results
• An Introduction to On-shell Recursion Relations
• Dual Conformal Symmetry, Integration-by-Parts Reduction, Differential Equations and the Nonplanar Sector
• The Multi-Regge limit of NMHV Amplitudes in N=4 SYM Theory
• Implications of nonplanar dual conformal symmetry
• Correlation functions, null polygonal Wilson loops, and local operators
• A study of Feynman integrals with uniform transcendental weights and the symbology from dual conformal symmetry
• Twistor actions for gauge theory and gravity
• Symbols of One-Loop Integrals From Mixed Tate Motives
• Global Poles of the Two-Loop Six-Point N=4 SYM integrand
• The Coulomb-branch S-matrix from massless amplitudes
• One-loop N = 4 super Yang-Mills scattering amplitudes in d dimensions, relation to open strings and polygonal Wilson loops
• Permutation Relations of Yangian Invariants, Unitarity Cuts, and Scattering Amplitudes
• 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
• Two-loop D-dimensional unitarity and dual conformal symmetry
• Scattering Amplitudes in Gauge Theories