The Yangian origin of the Grassmannian integral

Abstract

In this paper we analyse formulas which reproduce different contributions to scattering amplitudes in N=4 super Yang-Mills theory through a Grassmannian integral. Recently their Yangian invariance has been proved directly by using the explicit expression of the Yangian level-one generators. The specific cyclic structure of the form integrated over the Grassmannian enters in a crucial way in demonstrating the symmetry. Here we show that the Yangian symmetry fixes this structure uniquely.

26 pages. v2: typos corrected, published version

References in corpus (52)

• Gauge Theory Correlators from Non-Critical String Theory
• The Large N Limit of Superconformal Field Theories and Supergravity
• Direct Proof Of Tree-Level Recursion Relation In Yang-Mills Theory
• The Bethe-Ansatz for N=4 Super Yang-Mills
• One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits
• Perturbative Gauge Theory As A String Theory In Twistor Space
• Fusing Gauge Theory Tree Amplitudes Into Loop Amplitudes
• New Recursion Relations for Tree Amplitudes of Gluons
• Gluon scattering amplitudes at strong coupling
• Hidden Symmetries of the AdS_5 x S^5 Superstring
• Generalized Unitarity and One-Loop Amplitudes in N=4 Super-Yang-Mills
• The Dilatation Operator of Conformal N=4 Super Yang-Mills Theory
• 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
• 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
• 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
• Anti De Sitter Space And Holography
• Hexagon Wilson loop = six-gluon MHV amplitude
• A Duality For The S Matrix
• Fermionic T-Duality, Dual Superconformal Symmetry, and the Amplitude/Wilson Loop Connection
• Dual Superconformal Invariance, Momentum Twistors and Grassmannians
• Dual Superconformal Symmetry from AdS5 x S5 Superstring Integrability
• A note on dual superconformal symmetry of the N=4 super Yang-Mills S-matrix
• A Relation Between Approaches to Integrability in Superconformal Yang-Mills Theory
• Scattering into the fifth dimension of N=4 super Yang-Mills
• The Grassmannian Origin Of Dual Superconformal Invariance
• The hexagon Wilson loop and the BDS ansatz for the six-gluon amplitude
• The S-Matrix in Twistor Space
• All tree-level amplitudes in N=4 SYM
• Unification of Residues and Grassmannian Dualities
• 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
• Sharpening The Leading Singularity
• Yangians, Grassmannians and T-duality
• One-Loop Superconformal and Yangian Symmetries of Scattering Amplitudes in N=4 Super Yang-Mills
• On T-Duality and Integrability for Strings on AdS Backgrounds
• Symmetries and analytic properties of scattering amplitudes in N=4 SYM theory
• Recursion Relations, Generating Functions, and Unitarity Sums in N=4 SYM Theory
• Superconformal invariants for scattering amplitudes in N=4 SYM theory
• Twistor-Strings, Grassmannians and Leading Singularities
• Scattering Amplitudes and BCFW Recursion in Twistor Space
• Eliminating spurious poles from gauge-theoretic amplitudes
• Unraveling L_{n,k}: Grassmannian Kinematics
• T-Duality, Dual Conformal Symmetry and Integrability for Strings on AdS_5 x S^5
• Symmetries of the N=4 SYM S-matrix
• Twistor transform of all tree amplitudes in N=4 SYM theory

Cited by in corpus (68)

• Local Integrals for Planar Scattering Amplitudes
• Superconformal symmetry and two-loop amplitudes in planar N=4 super Yang-Mills
• Notes on the scattering amplitude / Wilson loop duality
• Jumpstarting the all-loop S-matrix of planar N=4 super Yang-Mills
• The super-correlator/super-amplitude duality: Part I
• Scattering Amplitudes
• Symmetries of Tree-level Scattering Amplitudes in N=6 Superconformal Chern-Simons Theory
• New differential equations for on-shell loop integrals
• Scattering Amplitudes and Wilson Loops in Twistor Space
• Superconformal invariants for scattering amplitudes in N=4 SYM theory
• Yang-Baxter operators and scattering amplitudes in $\mathcal{N}=4$ super-Yang-Mills theory
• Simple loop integrals and amplitudes in N=4 SYM
• Spectral Parameters for Scattering Amplitudes in N=4 Super Yang-Mills Theory
• Towards the Amplituhedron Volume
• The Grassmannian and the Twistor String: Connecting All Trees in N=4 SYM
• Star Integrals, Convolutions and Simplices
• Two-loop Octagons, Algebraic Letters and $\bar{Q}$ Equations
• Bethe Ansatz for Yangian Invariants: Towards Super Yang-Mills Scattering Amplitudes
• Bonus Yangian Symmetry for the Planar S-Matrix of N=4 Super Yang-Mills
• Efficient Tree-Amplitudes in N=4: Automatic BCFW Recursion in Mathematica
• On Yangian-invariant regularisation of deformed on-shell diagrams in N=4 super-Yang-Mills theory
• Descent equations for superamplitudes
• The symbol and alphabet of two-loop NMHV amplitudes from $\bar{Q}$ equations
• Symbol Alphabets from Plabic Graphs
• Integrable Amplitude Deformations for N=4 Super Yang-Mills and ABJM Theory
• Exact Superconformal and Yangian Symmetry of Scattering Amplitudes
• Cluster Adjacency for m=2 Yangian Invariants
• Yangian Invariants and Cluster Adjacency in N=4 Yang-Mills
• Grassmannians and form factors with $q^2=0$ in N=4 SYM theory
• Prescriptive Unitarity with Elliptic Leading Singularities
• Inverse Soft Factors and Grassmannian Residues
• Wilson lines, Grassmannians and Gauge Invariant Off-shell Amplitudes in N=4 SYM
• Symbol Alphabets from Plabic Graphs II: Rational Letters
• Cross-Order Integral Relations from Maximal Cuts
• An Elliptic Yangian-Invariant, `Leading Singularity'
• Hidden Simplicity of Gauge Theory Amplitudes
• Scattering Amplitudes and Toric Geometry
• Towards the Gravituhedron: New Expressions for NMHV Gravity Amplitudes
• The Three-loop MHV Octagon from $\bar{Q}$ equations
• Global Poles of the Two-Loop Six-Point N=4 SYM integrand
• The Grassmannian for Celestial Superamplitudes
• On the Classification of Residues of the Grassmannian
• Yangian Symmetry for the Tree Amplituhedron
• Multi-Particle Amplitudes from the Four-Point Correlator in Planar N=4 SYM
• Yangian in the Twistor String
• Tree-level scattering amplitudes from the amplituhedron
• Correlators with $s{\ell }_2$ Yangian symmetry
• One-loop N = 4 super Yang-Mills scattering amplitudes in d dimensions, relation to open strings and polygonal Wilson loops
• Yangian Symmetry in N=4 super Yang-Mills
• Grassmannian Integral for General Gauge Invariant Off-shell Amplitudes in N=4 SYM
• On All-loop Integrands of Scattering Amplitudes in Planar N=4 SYM
• Permutation Relations of Yangian Invariants, Unitarity Cuts, and Scattering Amplitudes
• Twistor and Polytope Interpretations for Subleading Color One-Loop Amplitudes
• Nonplanar On-shell Diagrams and Leading Singularities of Scattering Amplitudes
• Grassmannian Integrals as Matrix Models for Non-Compact Yangian Invariants
• Holonomies of gauge fields in twistor space 4: functional MHV rules and one-loop amplitudes
• Differential equations for multi-loop integrals and two-dimensional kinematics
• Boundary Perimeter Bethe Ansatz
• Yangian symmetry of light-like Wilson loops
• Commuting Conformal and Dual Conformal Symmetries in the Regge limit
• Grassmannian Integrals in Minkowski Signature, Amplitudes, and Integrability
• Weak Separation, Positivity and Extremal Yangian Invariants
• Perturbative Methods for Superconformal Quantum Field Theories in String - Gauge Theory Dualities
• Higher Codimension Singularities Constructing Yang-Mills Tree Amplitudes
• Symplectic Grassmannians, dual conformal symmetry and 4-point amplitudes in 6D
• Scattering Amplitudes in Gauge Theories
• On the Integrable Structure of Super Yang-Mills Scattering Amplitudes
• Brane Tilings as On-shell Diagrams