Harmonic R-matrices for Scattering Amplitudes and Spectral Regularization

Abstract

Planar N=4 super Yang-Mills appears to be integrable. While this allows to find this theory's exact spectrum, integrability has hitherto been of no direct use for scattering amplitudes. To remedy this, we deform all scattering amplitudes by a spectral parameter. The deformed tree-level four-point function turns out to be essentially the one-loop R-matrix of the integrable N=4 spin chain satisfying the Yang-Baxter equation. Deformed on-shell three-point functions yield novel three-leg R-matrices satisfying bootstrap equations. Finally, we supply initial evidence that the spectral parameter might find its use as a novel symmetry-respecting regulator replacing dimensional regularization. Its physical meaning is a local deformation of particle helicity, a fact which might be useful for a much larger class of non-integrable four-dimensional field theories.

4 pages, 5 figures; v2: minor changes, accepted for publication in Phys. Rev. Lett

References in corpus (13)

• Direct Proof Of Tree-Level Recursion Relation In Yang-Mills Theory
• New Recursion Relations for Tree Amplitudes of Gluons
• The N=4 SYM Integrable Super Spin Chain
• Long-Range PSU(2,2|4) Bethe Ansaetze for Gauge Theory and Strings
• Dual superconformal symmetry of scattering amplitudes in N=4 super-Yang-Mills theory
• The All-Loop Integrand For Scattering Amplitudes in Planar N=4 SYM
• The Dilatation Operator of N=4 Super Yang-Mills Theory and Integrability
• Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory
• A Duality For The S Matrix
• Dual Superconformal Invariance, Momentum Twistors and Grassmannians
• Scattering into the fifth dimension of N=4 super Yang-Mills
• From Scattering Amplitudes to the Dilatation Generator in N=4 SYM
• Hidden Simplicity of Gauge Theory Amplitudes

Cited by in corpus (47)

• The Amplituhedron
• Motivic Amplitudes and Cluster Coordinates
• Into the Amplituhedron
• Space-time S-matrix and Flux-tube S-matrix III. The two-particle contributions
• Space-time S-matrix and Flux-tube S-matrix IV. Gluons and Fusion
• Yangian Symmetry for Fishnet Feynman Graphs
• Lectures on Yangian Symmetry
• Yang-Baxter operators and scattering amplitudes in $\mathcal{N}=4$ super-Yang-Mills theory
• On-shell Diagrams, Graßmannians and Integrability for Form Factors
• Spectral Parameters for Scattering Amplitudes in N=4 Super Yang-Mills Theory
• Yangian Symmetry of smooth Wilson Loops in N=4 super Yang-Mills Theory
• Y-system for form factors at strong coupling in AdS5 and with multi-operator insertions in AdS3
• Amplitudes, Form Factors and the Dilatation Operator in $\mathcal{N}=4$ SYM Theory
• Towards the Amplituhedron Volume
• Bethe Ansatz for Yangian Invariants: Towards Super Yang-Mills Scattering Amplitudes
• The hexagon in the mirror: the three-point function in the SoV representation
• Secret Symmetries of Type IIB Superstring Theory on AdS3 x S3 x M4
• N=4 Scattering Amplitudes and the Deformed Grassmannian
• On Yangian-invariant regularisation of deformed on-shell diagrams in N=4 super-Yang-Mills theory
• A dictionary between R-operators, on-shell graphs and Yangian algebras
• Integrable Amplitude Deformations for N=4 Super Yang-Mills and ABJM Theory
• Novel construction and the monodromy relation for three-point functions at weak coupling
• Deformed Twistors and Higher Spin Conformal (Super-)Algebras in Six Dimensions
• String Bits and the Spin Vertex
• Yangian symmetric correlators
• 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
• On-shell diagrammatics and the perturbative structure of planar gauge theories
• Nonlocal Symmetries, Spectral Parameter and Minimal Surfaces in AdS/CFT
• Introduction to Integrability and One-point Functions in $\mathcal{N}=4$ SYM and its Defect Cousin
• Yangian Symmetry for the Tree Amplituhedron
• Positivity Sectors and the Amplituhedron
• On the singlet projector and the monodromy relation for psu(2, 2|4) spin chains and reduction to subsectors
• Correlators with $s{\ell }_2$ Yangian symmetry
• Non-Planar On-Shell Diagrams
• A Shortcut to General Tree-level Scattering Amplitudes in N=4 SYM via Integrability
• Grassmannian Integral for General Gauge Invariant Off-shell Amplitudes in N=4 SYM
• Anatomy of the Amplituhedron
• Logarithmic Singularities and Maximally Supersymmetric Amplitudes
• Grassmannian Integrals as Matrix Models for Non-Compact Yangian Invariants
• The DeWitt Equation in Quantum Field Theory
• Integrability As Duality: The Gauge/YBE Correspondence
• 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