On Yangian-invariant regularisation of deformed on-shell diagrams in N=4 super-Yang-Mills theory

Abstract

We investigate Yangian invariance of deformed on-shell diagrams with D=4, N=4 superconformal symmetry. We find that invariance implies a direct relationship between the deformation parameters and the permutation associated to the on-shell graph. We analyse the connection with deformations of scattering amplitudes in N=4 super-Yang-Mills theory and the possibility of using the deformation parameters as a regulator preserving Yangian invariance. A study of higher-point tree and loop graphs suggests that manifest Yangian invariance of the amplitude requires trivial deformation parameters.

32 pages; replaced with published version (updated abstract, minor corrections)

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• Dual Conformal Structure Beyond the Planar Limit
• N=4 Scattering Amplitudes and the Deformed Grassmannian
• Integrable Amplitude Deformations for N=4 Super Yang-Mills and ABJM Theory
• Deformed one-loop amplitudes in N = 4 super-Yang-Mills theory
• Cluster Algebras and the Positive Grassmannian
• Positivity Sectors and the Amplituhedron
• Non-Planar On-Shell Diagrams
• Correlators with $s{\ell }_2$ Yangian symmetry
• Anatomy of the Amplituhedron
• Permutation Relations of Yangian Invariants, Unitarity Cuts, and Scattering Amplitudes
• Logarithmic Singularities and Maximally Supersymmetric Amplitudes
• Top-forms of Leading Singularities in Nonplanar Multi-loop Amplitudes
• Grassmannian Integrals as Matrix Models for Non-Compact Yangian Invariants
• Nonplanar On-shell Diagrams and Leading Singularities of Scattering Amplitudes
• Grassmannian Integrals in Minkowski Signature, Amplitudes, and Integrability
• Yangian symmetry applied to Quantum chromodynamics
• QCD at high energies and Yangian symmetry
• On the Integrable Structure of Super Yang-Mills Scattering Amplitudes