A dictionary between R-operators, on-shell graphs and Yangian algebras

Abstract

We translate between different formulations of Yangian invariants relevant for the computation of tree-level scattering amplitudes in N=4 super-Yang--Mills theory. While the R-operator formulation allows to relate scattering amplitudes to structures well known from integrability, it can equally well be connected to the permutations encoded by on-shell graphs.

44 pages; replaced with published version

References in corpus (6)

• The All-Loop Integrand For Scattering Amplitudes in Planar N=4 SYM
• Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory
• All tree-level amplitudes in massless QCD
• MHV Diagrams in Momentum Twistor Space
• Harmonic R-matrices for Scattering Amplitudes and Spectral Regularization
• Bonus Yangian Symmetry for the Planar S-Matrix of N=4 Super Yang-Mills

Cited by in corpus (24)

• Space-time S-matrix and Flux-tube S-matrix IV. Gluons and Fusion
• Yangian Symmetry for Bi-Scalar Loop Amplitudes
• On-shell Diagrams, Graßmannians and Integrability for Form Factors
• Amplitudes, Form Factors and the Dilatation Operator in $\mathcal{N}=4$ SYM Theory
• The hexagon in the mirror: the three-point function in the SoV representation
• On Form Factors in N=4 SYM Theory and Polytopes
• N=4 Scattering Amplitudes and the Deformed Grassmannian
• Integrable Amplitude Deformations for N=4 Super Yang-Mills and ABJM Theory
• On Soft Theorems And Form Factors In N=4 SYM Theory
• Deformed one-loop amplitudes in N = 4 super-Yang-Mills theory
• Grassmannians and form factors with $q^2=0$ in N=4 SYM theory
• Wilson lines, Grassmannians and Gauge Invariant Off-shell Amplitudes in N=4 SYM
• Cluster Algebras and the Positive Grassmannian
• Color structures and permutations
• Yangian Symmetry for the Tree Amplituhedron
• On the singlet projector and the monodromy relation for psu(2, 2|4) spin chains and reduction to subsectors
• Grassmannian Integral for General Gauge Invariant Off-shell Amplitudes in N=4 SYM
• 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
• A connection between $\mathcal{R}$-invariants and Yang-Baxter $R$-operators in $\mathcal{N}=4$ super-Yang-Mills theory
• QCD at high energies and Yangian symmetry